pure-pixel assumption – Optimization Online

Robust Near-Separable Nonnegative Matrix Factorization Using Linear Optimization

Published: 2013/02/19

Data-Mining, Linear Programming hyperspectral unmixing, linear programming, nonnegative matrix factorization, pure-pixel assumption, robustness, separability

Nonnegative matrix factorization (NMF) has been shown recently to be tractable under the separability assumption, under which all the columns of the input data matrix belong to the convex cone generated by only a few of these columns. Bittorf, Recht, R\’e and Tropp (`Factoring nonnegative matrices with linear programs’, NIPS 2012) proposed a linear programming … Read more

Fast and Robust Recursive Algorithms for Separable Nonnegative Matrix Factorization

Published: 2012/08/06, Updated: 2012/08/10

Nicolas Gillis

Stephen A. Vavasis

Data-Mining hyperspectral unmixing, linear mixing model, nonnegative matrix factorization, pure-pixel assumption, robustness, separability

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 … Read more