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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf,len=887
+page_content='An improved hybrid regularization approach for extreme  learning machine  Liangjuan Zhou  School of Mathematics, Hunan University  Changsha, China  Wei Miao∗  miaow@hnu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='cn  School of Mathematics, Hunan University  Changsha, China  ABSTRACT  Extreme learning machine (ELM) is a network model that arbitrarily  initializes the first hidden layer and can be computed speedily.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  In order to improve the classification performance of ELM, a ℓ2  and ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5 regularization ELM model (ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM) is proposed in  this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' An iterative optimization algorithm of the fixed point  contraction mapping is applied to solve the ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The  convergence and sparsity of the proposed method are discussed  and analyzed under reasonable assumptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The performance of  the proposed ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM method is compared with BP, SVM, ELM,  ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM, ℓ1-ELM, ℓ2-ELM and ℓ2-ℓ1ELM, the results show that the  prediction accuracy, sparsity, and stability of the ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM are  better than the other 7 models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  CCS CONCEPTS  Mathematics of computing → Convex optimization;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' • Com-  puting methodologies → Regularization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  KEYWORDS  High-dimensional data, Sparsity, Hybird regularization, Dimension-  ality reduction  ACM Reference Format:  Liangjuan Zhou and Wei Miao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' An improved hybrid regularization  approach for extreme learning machine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' In 2022 4th International Conference  on Advanced Information Science and System (AISS 2022), November 25–27,  2022, Sanya, China.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' ACM, New York, NY, USA, 7 pages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  1145/3573834.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='3574501  1  INTRODUCTION  Feedforward neural networks(FNNs), as one of the most frequently  used neural networks which can be defined mathematically as:  𝐺𝑁 (𝑥𝑖) =  𝑁  ∑︁  𝑖=1  𝛽𝑖𝑔(⟨𝜔𝑖,𝑥𝑖⟩ + 𝑏𝑖),  where 𝑥𝑖 = (𝑥𝑖1,𝑥𝑖2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' ,𝑥𝑖𝑝) ∈ R𝑝 is the input, 𝑏𝑖 is the bias and 𝑔  is the activation function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' ⟨𝜔𝑖,𝑥𝑖⟩ = �𝑝  𝑗=1 𝜔𝑖𝑗𝑥𝑖𝑗 is the euclidean  ∗Both authors contributed equally to this research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Permission to make digital or hard copies of all or part of this work for personal or  classroom use is granted without fee provided that copies are not made or distributed  for profit or commercial advantage and that copies bear this notice and the full citation  on the first page.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Copyrights for components of this work owned by others than ACM  must be honored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Abstracting with credit is permitted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' To copy otherwise, or republish,  to post on servers or to redistribute to lists, requires prior specific permission and/or a  fee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Request permissions from permissions@acm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='org.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  AISS 2022, November 25–27, 2022, Sanya, China  © 2022 Association for Computing Machinery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  ACM ISBN 978-1-4503-9793-3/22/11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='$15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='1145/3573834.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='3574501  inner product, 𝜔𝑖 = (𝜔𝑖1,𝜔𝑖2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' ,𝜔𝑖𝑝) ∈ R𝑝 are the weights con-  necting the input and the 𝑖-th hidden node, and 𝛽𝑖 ∈ R are the  weights connecting the 𝑖-th hidden and output node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' In terms of  the traditional learning algorithm of FNNs, all parameters in the  network need to be adjusted based on specific tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' A classical  learning method is the backpropagation (BP) algorithm, which is  mainly solved by gradient descent:  min  𝜔𝑖,𝛽𝑖,𝑏𝑖  𝑛  ∑︁  𝑖=1  ∥𝑡𝑖 − 𝐺𝑁 (𝑥𝑖)∥2  2,  where (𝑥𝑖,𝑡𝑖)(𝑖 = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' ,𝑛) denotes the training samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' How-  ever, a randomized learner model, different to the traditional learn-  ing of FNNs, called as Extreme learning machine(ELM) and related  algorithms were proposed by Huang[10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' In the ELM model, 𝜔𝑖 and  𝑏𝑖 are randomly assigned without training, so only 𝛽𝑖 needs to be  trained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Set T = [𝑡1,𝑡2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' ,𝑡𝑛] and  H =  \uf8ee\uf8ef\uf8ef\uf8ef\uf8ef\uf8ef\uf8f0  𝑔(⟨𝜔1,𝑥1⟩ + 𝑏1)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  𝑔(⟨𝜔𝑁,𝑥1⟩ + 𝑏𝑁 )  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  𝑔(⟨𝜔1,𝑥𝑛⟩ + 𝑏1)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  𝑔(⟨𝜔𝑁,𝑥𝑛⟩ + 𝑏𝑁 )  \uf8f9\uf8fa\uf8fa\uf8fa\uf8fa\uf8fa\uf8fb  ,  (1)  once the input weights and biases are specified randomly with uni-  form distribution in [−𝑐,𝑐], the hidden output matrix remains un-  changed during the training phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Accordingly, the output weights  could be written by utilizing the least squares method:  min  𝛽 ∈R𝑁  �  ∥H𝛽 − T∥2  2  �  ,  (2)  the solution to model (2) could be written as 𝛽 = H†T, where H†  is the Moore–Penrose generalized inverse of hidden output matrix  H[14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  The theoretical basis for the general approximation capability of  ELM networks has been proposed and established by Igelnik[11] ,  where the range of randomly allocated input weights and biases  are data related and assigned in a constructive mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Consequently,  the scope of parameters in the algorithm implementation should  be carefully estimated for diverse datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' On the other hand,  considering the sparsity of the output parameter 𝛽 for many high-  dimensional data, Cao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' [4] proposed a ℓ1 regular ELM model  based on the sparsity of the ℓ1 regularization term, which takes the  following form:  min  𝛽 ∈R𝑁  � 1  2 ∥H𝛽 − T∥2  2 + 𝜆∥𝛽∥1  �  ,  (3)  where 𝜆 > 0 is a regularization parameter and 𝛽 is the output  coefficient calculated by iteration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' This model is called the Lasso  model, and has been studied by many scholars in recent years [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='01458v1  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='OC]  4 Jan 2023  AISS 2022, November 25–27, 2022, Sanya, China  Zhou and Miao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  For the model (2), Fan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' [8] added a ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5 regularization term  to the ELM model, based on the solution generated by ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5 is sparser  than the ℓ1 regularization term [16], and the model is defined as  follows:  min  𝛽 ∈R𝑁  � 1  2 ∥H𝛽 − T∥2  2 + 𝜆∥𝛽∥0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  �  ,  (4)  where 𝜆 > 0 is a regularization parameter, the model can be solved  by the iterative semi-threshold algorithm [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  The other regularization model for model (2) was about the ℓ2  regularization term (ℓ2-ELM) [5]:  min  𝛽 ∈R𝑁  � 1  2 ∥H𝛽 − T∥2  2 + 𝜇∥𝛽∥2  2  �  ,  (5)  where 𝜇 is a regularization parameter, and when the expression  H𝑇 H+𝜇I is invertible after choosing the parameter 𝜇, then the solu-  tion of the model (5) can be written as 𝛽 = (H𝑇 H + 𝜇I)−1I)−1H𝑇 T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Hai et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' [9] proposed a ℓ2-ℓ1-ELM hybrid model by integrating  the sparsity of the ℓ1 regularization term and the stability of the ℓ2  regularization term as follows:  min  𝛽 ∈R𝑁  � 1  2 ∥H𝛽 − T∥2  2 + 𝜆(𝛾∥𝛽∥1 + 𝜀∥𝛽∥2  2)  �  ,  (6)  where 𝜆 ≥ 0, 𝛾 ≥ 0 and 𝜀 ≥ 0 are regularization parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' In-  spired by the ℓ2-ℓ1-ELM model, according to Xu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' [17], they  found that the sparsity of the solution of the ℓ𝑝 (𝑝 ∈ (0, 1)) regular-  ization term: when 0 < 𝑝 < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5, there is no significant difference in  the sparse effect of ℓ𝑝;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' when 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5 < 𝑝 < 1, the smaller 𝑝, the better  the sparse effect, so the ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5 regularization term can be used as a  representative element of ℓ𝑝 (𝑝 ∈ (0, 1));' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Therefore, we propose the  ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM model by combining the stability of ℓ2 regularization  term and the sparsity of ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5 which is sparser than ℓ1, the new  model is described as:  min  𝛽 ∈R𝑁  � 1  2 ∥H𝛽 − T∥2  2 + 𝜆(𝛾∥𝛽∥0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5 + 𝜀∥𝛽∥2  2)  �  ,  (7)  where the parameters have the same meaning as the expression  of (6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The thought of adding ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5 and ℓ2 penalties simultaneously in  the optimization model could be found in classification [2, 6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' This  study mainly establishes an iterative algorithm and studies some  properties of randomized learner model as Hai[9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' In particular, we  integrate the features of ELM and propose an iterative strategy for  solving the hybrid model (7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The main contributions of this paper  can be summarized as follows:  (i) The whole model is a non-convex, non-smooth and non-  Lipschitz optimization problem due to the existence of ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5 norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  We propose a new algorithm called as an ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  This algorithm is proved to be effective by analyzing the sum mini-  mization problem of two convex functions with certain characteris-  tics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  (ii) The key theoretical properties such as convergence, sparsity  are derived to guarantee the feasibility of the proposed method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  (iii) Numerous experiments were carried out, including some  UCI datasets collected from experts and intelligent systems fields,  gene datasets and ORL face image datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Experimental results  show that the better performance of the proposed ℓ2- ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM  algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  The rest of this paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Section 2 reviews  some basic concepts and theories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Section 3 demonstrates the itera-  tive method by a fixed point equation and proposes a algorithm for  ℓ2 - ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' In Section 4, some theoretical results about  convergence and sparsity are analyzed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' In Section 5, experimental  results on UCI datasets, gene datasets and ORL face image datasets  are shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The conclusion is drawn in Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  2  PRELIMINARIES  In this section, we present some fundamental concepts and con-  vex optimization theorems primarily.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Initially, it is about the half-  thresholding function[16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' 𝒫(𝜆,𝑡) : R → R, 𝜆 > 0, which can be  written as:  𝒫(𝜆,𝑡) =  � 2  3𝑡  �  1 + cos  � 2(𝜋−𝜙 (𝑡))  3  ��  |𝑡| > 3  4𝜆  2  3  0  |𝑡| ≤ 3  4𝜆  2  3  ,  (8)  where 𝜙(𝑡) = arccos  �  𝜆  8 ( |𝑡 |  3 )− 3  2  �  , 𝜋 = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='14, and then the corre-  sponding half-thresholding operator half(𝜆, 𝛽) : R𝑁 → R𝑁 acts  component-wise as:  [half(𝜆, 𝛽)]𝑖 = 𝒫(𝜆, 𝛽𝑖).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  (9)  Next, we introduce one key characteristic of the half-thresholding  operator [7, 16]:  ∥half(𝜆,𝑡) − half(𝜆,𝑡 ′)∥ ≤ ∥𝑡 − 𝑡 ′∥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  (10)  Another crucial notion of convex optimization is the proximity  operator [12]:  prox𝜑𝛽 = arg min  �  ∥𝑢 − 𝛽∥2  2 + 𝜑(𝑢)  �  ,  where𝜙 is a real-valued convex function on R𝑁 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' A primary property  of the proximity operator is drawn in Proposition 1[7], which will  be utilized to prove our major result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Let 𝜑 be a real-valued convex function on R𝑁 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Suppose 𝜓 (·) = 𝜑 + 𝜌  2 ∥ · ∥2  2 + ⟨·,𝑢⟩ + 𝜎, where 𝑢 ∈ R𝑁 , 𝜌 ∈ [0, ∞),  𝜎 ∈ R, then  prox𝜓 𝛽 = prox𝜑/(1+𝜌) ((𝛽 − 𝑢)/(1 + 𝜌)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  (11)  3  SOLUTION: FIXED POINT ITERATIVE  ALGORITHM FOR THE MODEL  For the ELM, the output matrix H is a bounded linear operator from  R𝑁 to R𝑚 owing to the activation function 𝑔(·) ∈ (0, 1), which is  finite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' In order to further improve the accuracy and sparsity, we  employ the regularization model (7) to estimate the output weights  of the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' We define concisely as:  𝑝𝛾,𝜀 = 𝛾∥𝛽∥0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5 + 𝜀∥𝛽∥2  2,  where 𝜀, 𝛾 ≥ 0, 𝑝𝛾,𝜀 : R𝑁 → [0, ∞).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Then the model (7) can be  redefined as  min  𝛽 ∈R𝑁  � 1  2 ∥H𝛽 − T∥2  2 + 𝜆𝑝𝛾,𝜀  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  (12)  Furthermore, we introduce the following Lemma and Theorem  which will be utilized to solve our model:  An improved hybrid regularization approach for extreme learning machine  AISS 2022, November 25–27, 2022, Sanya, China  Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' For all 𝜆 > 0 and 𝛽 ∈ R𝑁 ,the half-thresholding operator  (8) can be described as:  half(𝜆, 𝛽) = arg min  𝑢  � 1  2 ∥𝑢 − 𝛽∥2  2 + 𝜆∥𝑢∥0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' For all 𝜆  >  0,𝛾  ≥  0,𝜀  ≥  0 and 𝛽  ∈  R𝑁 ,  half(  𝜆𝛾  1+2𝜀𝜆,  𝛽  1+2𝜀𝜆 ) is the proximity operator of 𝜆𝑝𝛾,𝜀 (𝛽).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Let 𝜆 > 0, 𝛾 ≥ 0, 𝜀 ≥ 0 and 𝛿 ∈ (0, ∞).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Then 𝛽 is  a minimizer of function (12) if and only if it meets the fixed point  equation:  𝛽 = half  �  𝛿𝜆𝛾  1 + 2𝜀𝜆𝛿 , (I − 𝛿H𝑇 H)𝛽 − 𝛿H𝑇 T  1 + 2𝜀𝜆𝛿  �  ,  (13)  where the unit operator I : R𝑁 → R𝑁 , the definition of H is shown  in (1), and H𝑇 represents the adjoint of H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Moreover, from the property of the proximity operator, we can  drive a precise statement for the Lipschitz constant of a contractive  map and the corresponding theorem as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Set 𝜆 > 0,𝛾 ≥ 0,𝜀 ≥ 0 and 𝛿 ∈ (0, ∞).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Suppose that  there exist two positive constants 𝜅0 and 𝜅, such that the norm of the  output matrix H shown in (1) of the hidden layer is finite by them,  namely 𝜅0 ≤ ∥H𝑇 H∥2 ≤ 𝜅, Thus 𝛽 is a minimizer of (12) if and  only if it is a fixed point of the Lipchitz map Γ : R𝑁 → R𝑁 , that is,  𝛽 = Γ𝛽 where  Γ𝛽 = half  �  𝛿𝜆𝛾  1 + 2𝜀𝜆𝛿 , (I − 𝛿H𝑇 H)𝛽 + 𝛿H𝑇 T  1 + 2𝜀𝜆𝛿  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  (14)  Selecting𝛿 =  2  𝜅0+𝜅 , the Lipschitz constant is finite by𝑞 = 1− 2𝜅0  𝜅 + 𝜅0  ≤  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' In particular, if 𝜅0 > 0, we can get Γ is a contractive map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Theorem 1 and Theorem 2 illustrate that the problem of ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-  ELM can be described as a fixed point algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Furthermore, the  next theorem will introduce the iterative procedure of the ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-  ELM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Suppose that 𝜅0 and 𝜅 are positive constants, such  that the norm of the output matrix H shown in (1) of the hidden  layer is finite by them, namely, 𝜅0 ≤ ∥H𝑇 H∥2 ≤ 𝜅, and the sequence  {𝛽}∞  𝑙=0 ⊆ R𝑁 is described iteratively as  𝛽𝑙 = half  �  𝛿𝜆𝛾  1 + 2𝜀𝜆𝛿 , (I − 𝛿H𝑁 H)𝛽𝑙−1 − 𝛿H𝑇 T  1 + 2𝜀𝜆𝛿  �  ,  (15)  where 𝑙 = 1, 2, 3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' , 𝜆 > 0,𝜀 > 0,𝛾 ≥ 0 and 𝛿 =  2  𝜅+𝜅0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Thus {𝛽𝑙 }∞  𝑙=0  strongly converges the minimizer of model (10) in spite of the choice  of 𝛽0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Remark 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' It is not difficult to obtain from the proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  ∥𝛽𝑙 − 𝛽∗∥2 ≤  𝜅 + 𝜅0  𝜅0(𝜅 + 𝜅0 + 4𝜀𝜆)  �𝜅 − 𝜅0  𝜅 + 𝜅0  �𝑙  ∥H𝑇 T∥2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Therefore, for each 𝜉 > 0, if  𝜅 + 𝜅0  𝜅0(𝜅 + 𝜅0 + 4𝜀𝜆)  �𝜅 − 𝜅0  𝜅 + 𝜅0  �𝑙  ∥𝛽1 − 𝛽0∥2 < 𝜉.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  namely,  𝑙 >  log  � ∥𝛽1−𝛽0 ∥2(𝜅+𝜅0)  𝜉𝜅0(𝜅+𝜅0+4𝜀𝜆)  �  log  � 𝜅+𝜅0  𝜅−𝜅0  �  ,  thus  ∥𝛽𝑙 − 𝛽∗∥2 < 𝜉.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  As a conclusion, the complete ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM algorithm is given in  Algorithm 1 which integrates the result of Theorem 3 and Remark  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Next section, we want give some properties of our proposed  algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Algorithm 1: the algorithm for ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM model  Input:Given  a  set  of  training  samples  𝒻  =  �  (𝑥𝑗,𝑡𝑗) : 𝑥𝑗 ∈ R𝑝,𝑡𝑗 ∈ R𝑚, 𝑗 = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' ,𝑛  �,  activation  func-  tion 𝑔, hidden node number 𝑁, the related regularization  parameters 𝜆 > 0, 𝛾 ≥ 0, 𝜀 ≥ 0, the corresponding parameter 𝛿,  and an acceptable error 𝜉.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Step 1: Randomly assign a proper scope for input weight 𝜔𝑖 and  bias 𝑏𝑖 (𝑖 = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' , 𝑁)  Step 2: Compute the hidden layer output matrix H;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Step  3:  Set  𝛽0  =  (0, 0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' , 0),  𝛽1  =  half(  𝛿𝜆𝛾  1 + 2𝜀𝜆𝛿 , (I − 𝛿H𝑇 H)𝛽0 + 𝛿H𝑇 T  1 + 2𝜀𝜆𝛿  ), and 𝑙𝑚𝑎𝑥 be a minimal  positive integer but larger than  log  � ∥𝛽1 − 𝛽0∥2(𝜅 + 𝜅0)  𝜉𝜅0(𝜅 + 𝜅0 + 4𝜀𝜆)  �  log  � 𝜅+𝜅0  𝜅−𝜅0  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Step 4: For 𝑙 = 1 : 𝑙𝑚𝑎𝑥  if 𝑙 ≥ 𝑙𝑚𝑎𝑥, stop;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  else 𝑙 := 𝑙 + 1 and update the 𝛽 as follows: 𝛽𝑙+1 =  half(  𝛿𝜆𝛾  1 + 2𝜀𝜆𝛿 , (I − 𝛿H𝑇 H)𝛽𝑙 + 𝛿H𝑇 T  1 + 2𝜀𝜆𝛿  ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  repeat Step 4, until that the desired output weight is ^𝛽 = 𝛽𝑚𝑎𝑥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Output: Return the output weights ^𝛽;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  4  SOME CHARACTERISTICS FOR ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM  For the new section, we want to discuss and analyze some key  characteristics of the estimator regarding ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM, such as the  convergence and sparsity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' 𝛽𝑙 strongly converges to the minimum value 𝛽∗ of  the minimization problem  min  𝛽 ∈R𝑁  � 1  2 ∥H𝛽 − T∥2  2 + 𝜆𝑝𝛾𝜀 (𝛽)  �  as 𝑙 → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  𝛽0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5 in the ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM is a highly significant part of the sparsity  of the solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Thus, we set the Theorem 5 as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Suppose 𝜆  >  0,𝛾  >  0, then the support of  half(  𝜆𝛾  1+2𝜀𝜆,  𝛽  1+2𝜀𝜆 ) is finite for any 𝛽 ∈ R𝑁 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Particularly, 𝛽∗ and 𝛽𝑙  are all finitely supported.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  If the regularization parameters 𝜆 and 𝛾 are fixed as some con-  stant values, then 𝛽∗ and 𝛽𝑙 have only a few finite nonzero coeffi-  cients, and hence the solution to (12) is sparse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  AISS 2022, November 25–27, 2022, Sanya, China  Zhou and Miao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Table 1: Details of the 6 datasets  Dataset  Type  Sapmple  Feature  Catagory  Austrian  UCI  690  14  2  Ionosphere  UCI  151  34  2  Balance  UCL  625  4  3  colon  gene  62  2000  2  DLBCL  gene  77  7129  2  ORL  image  400  10304  40  5  PERFORMANCE EVALUATION  In the new section, a succession of experiments, containing some  UCI benchmark datasets[9] and gene data, are carried out to demon-  strate the performance of the proposed ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' All  the experiments are performed in the Mac Pycharm environment  running on Quad-Core Intel Core i5, CPU (8 GB 2133 MHz LPDDR3)  processor with the speed of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='40GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The activation function of  networks used in the experiments is taken as sigmoid function  𝑔(𝑥) = 1/(1 + 𝑒−𝑥).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  The ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM model is compared with seven other models:  BP, SVM, ELM, ℓ2-ℓ1-ELM, ℓ2-ELM, ℓ1-ELM, ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' BP includes  only one hidden layer and output layer, and all parameters are  trained by back-propagation algorithm;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' ℓ1-ELM and ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM are  the simplified forms of ℓ2-ℓ1-ELM and ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  The activation function is defined as: 𝑔(𝑥) = 1/(1 + 𝑒−𝑥).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  In order to check the algorithm for ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM model, three real  classification datasets from the UCI machine learning repository  are considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The basic information of each dataset is shown in  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The average of 30 experimental validations was used as  the final result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' For these datasets, the sample size is fixed, but each  sample is randomly assigned as training or testing data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='1  Performance for UCI datasets  To validate the performance of the proposed ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM model,  three types of real classification datasets were used for the experi-  ments, including UCI[3], gene expression, and ORL face datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  The UCI machine learning repository (2013UCI) contains three  datasets: Austrian Credit Approval(Austrian), Ionosphere, and Bal-  ance Scale(Balance).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The gene expression datasets contain colon[1]  and DLBCL[13], both of which are binary datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Moreover, the  ORL face dataset includes 400 images divided into 40 categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Each category contains 10 images with different facial details and  each image size is 112 × 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The detail information of all datasets  are summarized in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' In addition, these data were obtained  from different application fields, and it is hoped that the ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-  ELM model can be analyzed from multiple perspectives by using  these data from different backgrounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  We repeat 30 trials and take the averages as the final results  on account of reducing the random error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' And the regularization  parameters are used to control the trade-off between the error and  the penalty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' For Austrian dataset, take the parameters ( ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM,  ℓ2-ℓ1-ELM : 𝜆 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='8,𝛾 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='1,𝜀 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='9) and for Ionosphere dataset,  take ( ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM, ℓ2-ℓ1-ELM : 𝜆 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='9,𝛾 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='05,𝜀 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='9) and  Balance Scale dataset, ( ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM : 𝜆 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='8,𝛾 = 1,𝜀 = 1, for ℓ2-ℓ1-  ELM : 𝜆 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='005,𝛾 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5,𝜀 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5), we set the acceptable error 𝜉 =  Table 2: Performance comparison of 8 models on 3 different  datasets  Datasets  Methods  Times(s)  Remaining Nodes  Accuracy(% ± %)  Austrain  BP  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='1751  600  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='58 ± 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='57  SVM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0448  —  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='14 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='98  ELM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0588  600  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='37 ± 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='08  ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='8542  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='76 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00  ℓ1-ELM  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='1648  118.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='38 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00  ℓ2-ELM  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='2735  600  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='36 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00  ℓ2-ℓ1-ELM  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='041  492.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='38 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00  ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5875  118.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='76 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00  Ionosphere  BP  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='1751  600  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='58 ± 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='57  SVM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0108  –  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='51 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='09  ELM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0003  600  91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='55 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='78  ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0487  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='96 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00  ℓ1-ELM  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='4755  115.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='9  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='24 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='06  ℓ2-ELM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0520  600  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='05 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='57  ℓ2-ℓ1-ELM  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='4093  437.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='84 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='98  ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0569  193  98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='01 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00  Balance  BP  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='3814  600  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='99 ± 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='26  SVM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0215  –  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='63 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='86  EL,M  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0008  600  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='72 ± 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='66  ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='1285  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='3  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='55 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00  ℓ1-ELM  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5074  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='9  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='47 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='66  ℓ2-ELM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='1579  600  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='55 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00  ℓ2-ℓ1-ELM  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='8678  246.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='4  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='10 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='35  ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0974  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='7  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='91 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0001, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='001, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0001 respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The number of hidden nodes in  the experiments is 600.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Table 2 shows the running time, the number  of nodes retained, and the accuracy of the test for each dataset for  the eight models (the standard deviation is kept to 4 significant  digits, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00 in the table indicates a standard deviation of less than  10−4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' These indices are used to measure the sparsity, stability and  effectiveness of the proposed method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The corresponding figures  on testing are shown as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  From the results of 1-3, we can see that the accuracy of the ELM  model is lower than all the regularized ELM models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The standard  deviation of the ELM model is higher than that of other regularized  ELM models, which indicates that the stability of the ELM model is  lower.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The accuracy of the ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM model at all nodes can be  compared with other regularized ELM models, and the accuracy at  most hidden nodes is higher than other comparable regularized ELM  models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' This indicates that the ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM model has consistently  good classification prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' In terms of the standard deviation  of different nodes, the ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM model is lower than the other  compared models, indicating that the classification accuracy of this  method is more stable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  We can see the performance of ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM in detail and draw  the following conclusions:  (i) In 3 datasets, the classification accuracy of the regularized  ELM methods (ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM, ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM, ℓ2-ℓ1-ELM, ℓ1-ELM, ℓ2-ELM)  are significantly higher than that of the BP, SVM and ELM methods,  indicating that the regularized ELM methods have better general-  ization performance, and the classification accuracy of ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM  methods is higher than that of other compared regularized ELM  methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  (ii) From the perspective of the number of remaining hidden  nodes, ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM has the lowest number of hidden nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' It is shown  An improved hybrid regularization approach for extreme learning machine  AISS 2022, November 25–27, 2022, Sanya, China  200  300  400  500  600  700  800  900  1000 1100 1200  Number of Hidden Nodes  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='55  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='65  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='70  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='75  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='80  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='85  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='90  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='95  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00  Testing accuracy  ELM  l0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  l1  l2  l2l1  l2l0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  200  300  400  500  600  700  800  900  1000 1100 1200  Number of Hidden Nodes  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='002  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='004  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='006  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='008  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='010  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='012  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='014  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='016  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='018  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='020  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='022  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='024  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='026  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='028  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='030  SDs of Testing  ELM  l0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  l1  l2  l2l1  l2l0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
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+page_content='5  Figure 3: Performance comparison of 6 models in the Balance dataset  that the ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5 or ℓ1-regularization term is beneficial to enhance the  sparsity of the hidden nodes of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Compared with the ℓ2-  ℓ1-ELM model, the ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM model adds the ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5 regularization  term to the model, which has a sparser solution and thus a better  generalization ability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  (iii) From the perspective of algorithm running time, the ELM  model runs in the shortest time (the ELM model can obtain the  analytic solution directly without iterative computation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' In com-  parison, the SVM model runs faster than all ELM methods with  regularity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Secondly, for the 5 regularized ELM models, the models  with ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5 regularization terms (ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM, ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM) are faster  than the models with ℓ1 regularization terms (ℓ1-ELM, ℓ2- ℓ1-ELM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='2  Performance for gene datasets  In this section, the performance of the ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM model is vali-  dated using the colon and DLBCL data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The training and testing sets  of each dataset were experimented in the ratio of 1 : 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The regular-  ization parameters are set as follows, colon data: (ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM and  ℓ2-ℓ1-ELM : 𝜆 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='09,𝛾 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='9,𝜀 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='9), DLBCL data: (ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM  and ℓ2-ℓ1-ELM : 𝜆 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='005,𝛾 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5,𝜀 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' and 𝜉 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
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+page_content=' Each  dataset was repeatedly run 30 times, and the average was taken as  the final result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' As shown in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  It can be demonstrated that the prediction accuracy of the single-  layer BP network is very low and does not capture the features of  AISS 2022, November 25–27, 2022, Sanya, China  Zhou and Miao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
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+page_content='86  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='87  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='88  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='89  Testing accuracy  ELM  l0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  l1  l2  l2l1  l2l0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  200  300  400  500  600  700  800  900  1000 1100 1200  Number of Hidden Nodes  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='005  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='010  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='015  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='020  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='025  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='030  SDs of Testing  ELM  l0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  l1  l2  l2l1  l2l0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  Figure 4: Performance comparison of 6 models in colon dataset  Table 3: Performance comparison of 8 models in 2 gene  datasets  Datasets  Methods  Times(s)  Remaining Nodes  Accuracy(% ± %)  colon  BP  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='2641  1000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='52 ± 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='15  SVM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0358  –  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5 ± 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='28  ELM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0056  1000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='02 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='92  ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0829  370.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00  ℓ1-ELM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0488  974.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='79 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='22  ℓ2-ELM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0815  1000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='17 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='20  ℓ2-ℓ1-ELM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0401  1000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='96 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='24  ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0879  877.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='50 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00  DLBCL  BP  122.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='3174  1000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='24 ± 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='55  SVM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0968  –  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='24 ± 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='98  ELM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0060  786.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='90 ± 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='98  ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='2214  242.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0  91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='43 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00  ℓ1-ELM  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='2957  188.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='05 ± 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='12  ℓ2-ELM  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='2324  764.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='51 ± 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='48  ℓ2-ℓ1-ELM  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5286  431.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='62 ± 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='10  ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='4519  575.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5  91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='43 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00  the data very well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' It can also be found that the prediction accu-  racy of the ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM model is slightly higher than that of the  other methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The standard deviations of the accuracy of the ELM  methods with ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5 regularization are much smaller than those of  BP, SVM, and ELM, indicating that the ELM model variants with  ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5 regularization terms can improve the stability of the solutions;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  The number of hidden nodes in the ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM and ℓ1-ELM models  is smaller, that is, the sparsity of these two regularization terms is  the strongest, indicating that the addition of ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5 or ℓ1 regularization  terms in the ELM model enhances the sparsity of the model, while  the number of hidden nodes in the ℓ2-ELM model is 1000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The  number of nodes in the ℓ2-ELM model is 1000, indicating that the  ℓ2-regularization term has no sparse effect on the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The ℓ2  norm is used to increase the stability of the model by penalizing  oversized regularization parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' This makes the ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM  sparser and model stable, and thus obtains better generalization  ability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  From the perspective of algorithm running time, it can be seen  that the ELM model has the shortest running time (the ELM model  can obtain the analytical solution directly without iterative solving).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  In contrast, the SVM model runs faster than all ELM methods with  regularization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Further, we use the colon data to verify the effect of different  number of hidden nodes (200, 400, 600, 800, 1000, 1200) on the sta-  bility of the ELM correlation model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' We perform 30 experiments  for each hidden node and calculate the ELM, ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM, ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM,  ℓ2-ℓ1-ELM, ℓ1-ELM, ℓ2-ELM for the test set accuracy and standard  deviation as shown in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The test accuracy of ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM at  all nodes can be compared with all regularized ELM models, while  the accuracy at most hidden nodes is higher than other models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  The standard deviation of ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM model is lower than other  regularized ELM models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='3  Performance for ORL face dataset  The ORL face dataset is used for experimental validation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The num-  ber of hidden nodes for the experiment is 1000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The average of  30 experiments is used as the final result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Since the original im-  age has high dimensionality, we preprocess each image by using  the (2𝐷)2PCA[18] dimensionality reduction technique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' And the  training set and test set are in the ratio of 7 : 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The values of the  regular parameters set in the experiment are as follows: ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM  and ℓ1-ELM (𝛾 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='05,𝜀 = 0), ℓ2-ELM (𝛾 = 0,𝜀 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5), ℓ2 -ℓ1-ELM,  ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM(𝛾 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='05,𝜀 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' 𝜆 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='001 and 𝜀 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='0001 are cho-  sen in all experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' This experiment validates the performance  of the model in terms of accuracy and standard deviation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The re-  sults are shown in Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' From the table, it can be seen that the  Table 4: Performance comparison of 8 models in ORL face  dataset  Methods  Accuracy(%)  BP  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00 ± 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='90  SVM  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='53 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='12  ELM  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='58 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='95  ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='34  ℓ1-ELM  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='85 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='86  ℓ2-ELM  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='17 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='47  ℓ2-ℓ1-ELM  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='58 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='87  ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='67 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='34  An improved hybrid regularization approach for extreme learning machine  AISS 2022, November 25–27, 2022, Sanya, China  Table 5: Performance comparison of 6 models in ORL face dataset  Nodes  ELM  ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM  ℓ1-ELM  ℓ2-ELM  ℓ2-ℓ1-ELM  ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM  500  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='92±3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='04  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='10±2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='55  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00 ±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='77  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='63± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='38  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='25 ±2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='32  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='83 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='46  1500  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='08±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='73  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='93  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='33 ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='67  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='75± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='75  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='33 ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='76  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='20 ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='93  2000  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='25±2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='73±2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='45  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='33 ±2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='08  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='63± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='18  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='33 ±2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='08  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='83 ±2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='45  2500  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='58±3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='49  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='74±3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='36  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='67 ±3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='44  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='21±3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='29  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='63 ±3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='44  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='76 ± 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='26  3000  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='50±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='98  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='55±2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='69  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='42 ±2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='07  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='45±2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='39  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='42 ±2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='07  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='58 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='68  3500  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='17±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='81  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='13±2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='22  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='17 ±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='87  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='17±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='89  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='17 ±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='87  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='25 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='12  4000  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='81  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='67  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='92 ±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='74  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='96±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='64  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='92 ±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='74  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='08 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='65  mean  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='22±9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='12  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='16±5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='33  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='21 ±7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='62±6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='21  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='08 ±7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='24  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='26 ± 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='32  accuracy of the ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM model (which is slightly higher than  the SVM model) is slightly higher than all other models tested.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Further, we verify the effect of different values of hidden nodes  on the prediction accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The number of hidden nodes chosen in  the experiment is 500, 1000, 1500, 2000, 2500, 3000, 3500, 4000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  The results are shown in Table 5, which show that the test accu-  racy of ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM model is higher than the other comparative  ELM models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The test accuracy of the ELM model fluctuates the  most with the changing of the number of hidden nodes, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=', the  selection of different nodes has the greatest impact on it, indicating  that the ELM model is less stable in high-dimensional data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' In con-  trast, the standard deviations of all the regularized ELM methods  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='33, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='00, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='21, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='24, 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='32) are lower than those of the ELM meth-  ods, indicating that the stability of the ELM model is improved by  adding the regularization term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' ELM methods, indicating that the  stability of the proposed method is better than the other 5 compared  to ELM methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  6  CONCLUSION  In order to further improve the stability and generalization of the  ELM model, this paper proposes a ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM model by combin-  ing the ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5 and the ℓ2 regularization term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The iterative algorithm  is applied to solve the model with a fixed points algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' The  convergence and sparsity of this algorithm are proved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Moreover,  the proposed ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM model is compared with BP, SVM, ELM,  ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM, ℓ1-ELM, ℓ2-ELM and ℓ2-ELM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' ℓ2-ℓ1-ELM models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Experi-  mental comparisons on several datasets (UCI dataset, gene dataset,  ORL face dataset) show that the ℓ2-ℓ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='5-ELM method outperforms  the other 7 models in terms of prediction accuracy and stability  on these data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Therefore, the model can be improved as follows:  the information of previously computed nodes is not used in the  computation of different hidden nodes, and it can be learned from  the incremental learning point of view, which can reduce the com-  putation time to a certain extent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
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+page_content=' Kraaijveld, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
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+page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Duin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' 1992.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  Feedforward neural  networks with random weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' (1992), 1–4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  [15] Robert Tibshirani.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Regression shrinkage and selection via the lasso: a retro-  spective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Journal of the Royal Statistical Society: Series B (Statistical Methodology)  73, 3 (2011), 267–288.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='  [16] Zongben Xu, Xiangyu Chang, Fengmin Xu, and Hai Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' 𝐿1/2 regular-  ization: a thresholding representation theory and a fast solver.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' IEEE Transac-  tions on Neural Networks and Learning Systems 23, 7 (2012), 1013–1027.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' https:  //doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='1109/TNNLS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content='2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
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+page_content=' Representative  of 𝐿1/2 regularization among 𝐿𝑞 (0 < 𝑞 ≤ 1) regularizations: an experimental  study based on phase diagram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Acta Automatica Sinica 38, 7 (2012), 1225–1228.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
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+page_content=' 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' (2D)2PCA: Two-directional two-  dimensional PCA for efficient face representation and recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}
+page_content=' Neurocom-  puting 69, 1 (2005), 224–231.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5NAzT4oBgHgl3EQffvy-/content/2301.01458v1.pdf'}