A Very Fast Algorithm for Matrix Factorization

TL;DR

This paper introduces a highly efficient gradient-based algorithm for matrix factorization, enabling fast dimension reduction in high-dimensional data analysis, with demonstrated effectiveness in bioinformatics classification tasks.

Contribution

The paper proposes a novel, fast gradient-based matrix factorization algorithm applicable to any differentiable loss function, improving speed and flexibility over existing methods.

Findings

Demonstrated high speed in matrix factorization tasks.

Effective in reducing dimensions for high-dimensional bioinformatics data.

Improved classification performance in real datasets.

Abstract

We present a very fast algorithm for general matrix factorization of a data matrix for use in the statistical analysis of high-dimensional data via latent factors. Such data are prevalent across many application areas and generate an ever-increasing demand for methods of dimension reduction in order to undertake the statistical analysis of interest. Our algorithm uses a gradient-based approach which can be used with an arbitrary loss function provided the latter is differentiable. The speed and effectiveness of our algorithm for dimension reduction is demonstrated in the context of supervised classification of some real high-dimensional data sets from the bioinformatics literature.