Refinement of Hottopixx Method for Nonnegative Matrix Factorization Under Noisy Separability

TL;DR

This paper introduces a refined version of the Hottopixx algorithm for nonnegative matrix factorization that does not require prior noise level estimation, maintaining robustness in noisy separability scenarios.

Contribution

The authors propose a noise-level independent refinement of Hottopixx, enhancing its practicality and robustness for separable NMF applications.

Findings

Maintains robustness to noise without needing noise level estimation

Comparable noise robustness to original Hottopixx algorithm

Improves applicability in real-world noisy data scenarios

Abstract

Hottopixx, proposed by Bittorf et al. at NIPS 2012, is an algorithm for solving nonnegative matrix factorization (NMF) problems under the separability assumption. Separable NMFs have important applications, such as topic extraction from documents and unmixing of hyperspectral images. In such applications, the robustness of the algorithm to noise is the key to the success. Hottopixx has been shown to be robust to noise, and its robustness can be further enhanced through postprocessing. However, there is a drawback. Hottopixx and its postprocessing require us to estimate the noise level involved in the matrix we want to factorize before running, since they use it as part of the input data. The noise-level estimation is not an easy task. In this paper, we overcome this drawback. We present a refinement of Hottopixx and its postprocessing that runs without prior knowledge of the noise level. We show that the refinement has almost the same robustness to noise as the original algorithm.