Identification of NMF by choosing maximum-volume basis vectors

TL;DR

This paper introduces a maximum-volume-constrained NMF framework that enhances basis vector distinctiveness, overcoming limitations of minimum-volume-constrained NMF in highly mixed data scenarios.

Contribution

The paper proposes a novel maximum-volume-constrained NMF method with an identifiability theorem and an algorithm, improving basis interpretability and robustness.

Findings

Effective in highly mixed data scenarios

Basis vectors are more distinct and interpretable

Outperforms existing methods in experiments

Abstract

In nonnegative matrix factorization (NMF), minimum-volume-constrained NMF is a widely used framework for identifying the solution of NMF by making basis vectors as similar as possible. This typically induces sparsity in the coefficient matrix, with each row containing zero entries. Consequently, minimum-volume-constrained NMF may fail for highly mixed data, where such sparsity does not hold. Moreover, the estimated basis vectors in minimum-volume-constrained NMF may be difficult to interpret as they may be mixtures of the ground truth basis vectors. To address these limitations, in this paper we propose a new NMF framework, called maximum-volume-constrained NMF, which makes the basis vectors as distinct as possible. We further establish an identifiability theorem for maximum-volume-constrained NMF and provide an algorithm to estimate it. Experimental results demonstrate the effectiveness of the proposed method.