Question about SLIM MSE

[myui]

Hi @MaurizioFD ,

thanks sharing an interesting recsys course materials!

I have question about SLIM MSE in https://github.com/MaurizioFD/RecSys_Course_AT_PoliMi/blob/master/Practice%2006%20-%20SLIM%20MSE%20with%20Gradient%20Descent%20and%20Cython.ipynb

It describes

Which item similarities we modify? Only those we used to compute the prediction, i.e., only the items in the profile of the sampled user.

and only user interacted item weight is updated in your implementation. Is this implementation correct?

            # Compute prediction
            start_profile = URM_train_indptr[user_id]
            end_profile = URM_train_indptr[user_id+1]

            # Update model, in this case the similarity
            for index in range(start_profile, end_profile):
                profile_item_id = URM_train_indices[index]
                profile_rating = URM_train_data[index]
                item_item_S[profile_item_id,item_id] += learning_rate * (prediction_error * profile_rating - 
                                                                         regularization_2 * item_item_S[profile_item_id,item_id])
           item_item_S[item_id,item_id] = 0.0

user	item	rating
u1	i1	5.0
u1	i2	2.0
u1	i3	3.0
u2	i1	4.0

i3, i2 should similar be i1 as user a interacted with i2 and i3 along with i1. However, user B does not interacted other item to i1, no updates is being done with this scheme. ~Also, only (i1, i2), (i1,i3), (i2,i3) is updated for item_item_S and similarity like (3,1) is not updated.~ (i2,i1),(i3,i1),(i3,i2) is also updated.

The original SLIM paper and it's implementation uses kNN not to update all.

MyMediaLite and LibRec optimized to use kNN in training while it's coordinate descent though.

[myui]

when avoiding regularization term, no user-item interaction in URM (ratings_in_user_profile=0) gives item_item_S[profile_item_id,item_id] = 0 and thus skipping (?).

    # Update model, in this case the similarity
    items_in_user_profile = URM_train.indices[URM_train.indptr[user_id]:URM_train.indptr[user_id+1]]
    ratings_in_user_profile = URM_train.data[URM_train.indptr[user_id]:URM_train.indptr[user_id+1]]
    item_item_S[items_in_user_profile,item_id] += learning_rate * (prediction_error * ratings_in_user_profile -
                                                                   regularization_2 * item_item_S[items_in_user_profile,item_id])