Robustness Analysis of Hottopixx, a Linear Programming Model for Factoring Nonnegative Matrices
Year: 2013
Type: article
Abstract: Although nonnegative matrix factorization (NMF) is NP-hard in general, it has been shown very recently that it is tractable under the assumption that the input nonnegative data matrix is close to being separable. (Separability requires that all columns of the input matrix belong to the cone spanned by a small subset of these columns.) Since then, several algorithms have been designed to handle this subclass of NMF problems. In particular, Bittorf et al. [Adv. Neural Inform. Process. Syst., 25 (2012), pp. 1223--1231] proposed a linear programming model, referred to as Hottopixx. In this paper, we provide a new and more general robustness analysis of their method. In particular, we design a provably more robust variant using a postprocessing strategy which allows us to deal with duplicates and near duplicates in the data set.
Author: Nicolas Gillis
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1969013340