Group-sparse Embeddings in Collective Matrix Factorization

TL;DR

This paper introduces a novel collective matrix factorization method that models separate and shared low-rank structures across matrices, automatically inferring their nature using group sparsity, and supports diverse data types efficiently.

Contribution

It proposes a new CMF approach allowing independent and shared low-rank structures with automatic inference of their nature via group sparsity, handling various data types.

Findings

Model automatically infers the nature of each factor.

Supports continuous, binary, and count data.

Efficient for sparse matrices with missing data.

Abstract

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.