Update benchmarks/models/itemknn/README.md (#8)

- Update benchmarks/models/itemknn/README.md (e8b04458db77e2fb30a24e65f78923fa48b7d297)


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

benchmarks/models/itemknn/README.md

@@ -1,10 +1,10 @@
 # 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. 
+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).
 
-The formulation is: \\(score(user_i, item_j) = \cos(V[i, :], U[:,j])\\), 
+The formulation is: \\(score(user_i, item_j) = \cos(V[i,:], U^\top[j,:])\\), 
 
 where:
 
@@ -12,7 +12,7 @@ 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[:, k]^T\\)
+  \\(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
@@ -22,9 +22,5 @@ where:
 The hyperparameter `hour` defines the time period (in hours) associated with a decay factor of 0.9.
 
 
-## Memory Optimization
-
-For 5b datasets, the matrix multiplications between [num users \\(\times\\) num item] and [num item \\(\times\\) num items] exceeds memory constraints. 
-
-To solve this, we leverage cosine similarity to the mean embedding instead of pairwise similarities to avoid new dimension (x basket_size).
+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].