33. Process SVD Define the original user-item matrix, R, of size m x n, which includes the ratings of m users on n items. rij refers to the rating of user ui on item ij . Preprocess user-item matrix R in order to eliminate all missing data values. Compute the SVD of R and obtain matrices U, S and V , of size m x m, m x n, and n x n, respectively. Their relationship is expressed by: R =U * S * VT . Perform the dimensionality reduction step by keeping only k diagonal entries from matrix S to obtain a k x k matrix, Sk. Similarly, matrices Uk and Vk of size m x k and k x n are generated. The "reduced" user-item matrix, R’, is obtained by R’ = Uk * Sk * VkT, while r'ij denotes the rating by user ui on item ij as included in this reduced matrix. Compute sqrt(Sk) and then calculate two matrix products: Uk * sqrt(Sk)T, which represents m users and sqrt(Sk) * VkT , which represents n items in the k dimen-sional feature space. We are particularly interested in the latter matrix, of size k x n. Use KNN on user matrix and item matrix, or you can multiply them to get user's rating on every item.
34. Demo Which two people have the most similar tastes? Which two season are the most close? from Here