Fast and Robust Recursive Algorithms for Separable Nonnegative Matrix Factorization

TL;DR

This paper introduces a family of fast, recursive algorithms for separable nonnegative matrix factorization, providing theoretical robustness guarantees and unifying several existing hyperspectral unmixing methods.

Contribution

It presents a new family of algorithms with proven robustness, generalizing and theoretically justifying the superior practical performance of existing hyperspectral unmixing techniques.

Findings

Algorithms are robust under small data perturbations

The family generalizes existing hyperspectral unmixing methods

Provides theoretical justification for practical performance

Abstract

In this paper, we study the nonnegative matrix factorization problem under the separability assumption (that is, there exists a cone spanned by a small subset of the columns of the input nonnegative data matrix containing all columns), which is equivalent to the hyperspectral unmixing problem under the linear mixing model and the pure-pixel assumption. We present a family of fast recursive algorithms, and prove they are robust under any small perturbations of the input data matrix. This family generalizes several existing hyperspectral unmixing algorithms and hence provides for the first time a theoretical justification of their better practical performance.