Update benchmarks/models/itemknn/README.md (#9)

- Update benchmarks/models/itemknn/README.md (b135b95e26949729529cab0f73d419bef7af9376)


Co-authored-by: Vladimir <[email protected]>

benchmarks/models/itemknn/README.md

@@ -1,10 +1,12 @@
 # ItemKNN
 
-We employ cosine similarity to measure similarity between vectors. Item vectors are represented as (num users)-dimensional vectors derived from the user-item interaction matrix, where component \\(d\\) represents how many times user \\(d\\) interacted with this item. 
 
-Top-k recommendations are generated by retrieving vectors closest to the user's temporal interaction pattern (with decay parameter \\(\tau \rightarrow 0\\)) controlling historical influence).
+For this approach item vectors are represented as user-frequency [num users]-dimensional vectors constructed from the user-item interaction matrix \\(U\\). 
+\\(U_{ij}\\) indicates how many times user \\(i\\) interacted with the item \\(j\\).
 
-The formulation is: \\(score(user_i, item_j) = \cos(V[i,:], U^\top[j,:])\\), 
+### Similarity Measurement
+
+We employ cosine similarity to measure similarity between vectors: \\(score(user_i, item_j) = \cos(V_i, U^\top_j)\\)
 
 where:
 
@@ -12,15 +14,19 @@ where:
 
 - \\(V\\) [num users \\(\times\\) num users]: user embedding matrix, where each row is:
 
-  \\(V[i, :] = \sum_{(t, k) \in A_i} \tau^{\max_t(i) - t} U^\top[k, :]\\)
+  \\(V_{i} = \sum_{(t, k) \in A_i} \tau^{\max_t(i) - t} U^\top_{k}\\)
 
     - \\(A_i\\): set of \\(i\\)-th user's (interaction timestamp, item index) pairs
     - \\(\max_t(i)\\): last \\(i\\)-th user's interaction timestamp
     - \\(\tau\\): time decay coefficient (per second)
 
+For instance, when \\(\tau\\) is equal to 0 (which is the simplest case), Top-k recommendations are generated by retrieving the most closest (k) item embeddings to the latest user's representation.
 
-The hyperparameter `hour` defines the time period (in hours) associated with a decay factor of 0.9.
+### Hyperparameters
 
+Parameter `hour` defines the time period (in hours) associated with a decay factor of 0.9.
 
-For 5b datasets, the results are not provided due to exceeding of memory constraints caused by matrix multiplications between [num users \\(\times\\) num item] and [num item \\(\times\\) num items]. 
+### Implementation Note
 
+For 5b-scale datasets, memory constraints arise when multiplying user-item interaction matrix \\(U\\) and the user embedding matrix making computations infeasible. 
+Thus, results for these datasets are not provided.