Group-sparse Embeddings in Collective Matrix Factorization
This addresses a limitation in CMF for applications like recommender systems, though it appears incremental as it builds on existing CMF frameworks.
The authors tackled the problem of collective matrix factorization (CMF) breaking down when matrices have low-rank structures not shared with others, by presenting a novel solution that allows separate and subset-shared low-rank structures, with results showing the model automatically infers factor nature using group-wise sparsity.
CMF is a technique for simultaneously learning low-rank representations based on a collection of matrices with shared entities. A typical example is the joint modeling of user-item, item-property, and user-feature matrices in a recommender system. The key idea in CMF is that the embeddings are shared across the matrices, which enables transferring information between them. The existing solutions, however, break down when the individual matrices have low-rank structure not shared with others. In this work we present a novel CMF solution that allows each of the matrices to have a separate low-rank structure that is independent of the other matrices, as well as structures that are shared only by a subset of them. We compare MAP and variational Bayesian solutions based on alternating optimization algorithms and show that the model automatically infers the nature of each factor using group-wise sparsity. Our approach supports in a principled way continuous, binary and count observations and is efficient for sparse matrices involving missing data. We illustrate the solution on a number of examples, focusing in particular on an interesting use-case of augmented multi-view learning.