Collaborative Filtering and Heavy-Tailed Degree Distributions

Common techniques in collaborative filtering rely on finding low-rank matrix approximations to the adjacency matrix (ratings that users assign to items), essentially representing users and items as a collection of a small number of latent features. One issue that arises in many real world datasets for collaborative filtering is that the number of observed entries per row/column follows a heavy-tail distribution. For instance, in the Amazon product ratings dataset, the maximum degree of a product is 12180 whereas the average number of ratings for each product is 4.68. We show that these over-represented rows/columns alter the spectrum of the adjacency matrix significantly, which negatively affects the performance of SVD based methods for low-rank approximations. Further, we present experimental evaluation to show that discarding rows/columns with high degree results in improved performance accross several different datasets (Amazon products ratings, movie ratings and book ratings).