Neural Network Matrix Factorization

TL;DR

Neural network matrix factorization (NNMF) replaces the traditional inner product in matrix factorization with a learnable neural network, improving performance on benchmarks but still has room for further development.

Contribution

This paper introduces NNMF, a novel approach that learns a flexible function to replace the inner product in matrix factorization using neural networks.

Findings

NNMF outperforms standard low-rank techniques on benchmarks

The approach is dominated by some recent graph-based methods

Potential exists for further improvements with different architectures

Abstract

Data often comes in the form of an array or matrix. Matrix factorization techniques attempt to recover missing or corrupted entries by assuming that the matrix can be written as the product of two low-rank matrices. In other words, matrix factorization approximates the entries of the matrix by a simple, fixed function---namely, the inner product---acting on the latent feature vectors for the corresponding row and column. Here we consider replacing the inner product by an arbitrary function that we learn from the data at the same time as we learn the latent feature vectors. In particular, we replace the inner product by a multi-layer feed-forward neural network, and learn by alternating between optimizing the network for fixed latent features, and optimizing the latent features for a fixed network. The resulting approach---which we call neural network matrix factorization or NNMF, for short---dominates standard low-rank techniques on a suite of benchmark but is dominated by some recent proposals that take advantage of the graph features. Given the vast range of architectures, activation functions, regularizers, and optimization techniques that could be used within the NNMF framework, it seems likely the true potential of the approach has yet to be reached.