Tight Semi-Nonnegative Matrix Factorization

TL;DR

This paper introduces a new matrix factorization method that uses conical combinations of templates to approximate data, allowing more flexible template selection without the nonnegativity constraint.

Contribution

It proposes a multi-objective optimization framework for matrix factorization that relaxes nonnegativity and convexity constraints on templates, enhancing flexibility.

Findings

Enables approximation of data with more flexible templates.

Does not require templates to be nonnegative or convex.

Focuses on data-specific template selection.

Abstract

The nonnegative matrix factorization is a widely used, flexible matrix decomposition, finding applications in biology, image and signal processing and information retrieval, among other areas. Here we present a related matrix factorization. A multi-objective optimization problem finds conical combinations of templates that approximate a given data matrix. The templates are chosen so that as far as possible only the initial data set can be represented this way. However, the templates are not required to be nonnegative nor convex combinations of the original data.