Robustness Analysis of Preconditioned Successive Projection Algorithm for General Form of Separable NMF Problem

Abstract

The successive projection algorithm (SPA) has been known to work well for separable nonnegative matrix factorization (NMF) problems arising in applications, such as topic extraction from documents and endmember detection in hyperspectral images. One of the reasons is in that the algorithm is robust to noise. Gillis and Vavasis showed in [SIAM J. Optim., 25(1), pp. 677-698, 2015] that a preconditioner can further enhance its noise robustness. The proof rested on the condition that the dimension $d$ and factorization rank $r$ in the separable NMF problem coincide with each other. However, it may be unrealistic to expect that the condition holds in separable NMF problems appearing in actual applications; in such problems, $d$ is usually greater than $r$. This paper shows, without the condition $d=r$, that the preconditioned SPA is robust to noise.

19 pages

References in corpus (6)

• Proceedings of the 29th International Conference on Machine Learning (ICML-12)
• Fast and Robust Recursive Algorithms for Separable Nonnegative Matrix Factorization
• Learning Topic Models - Going beyond SVD
• Semidefinite Programming Based Preconditioning for More Robust Near-Separable Nonnegative Matrix Factorization
• Ellipsoidal Rounding for Nonnegative Matrix Factorization Under Noisy Separability
• Enhancing Pure-Pixel Identification Performance via Preconditioning

Cited by in corpus (2)

• Introduction to Nonnegative Matrix Factorization
• Consistent Estimation of Mixed Memberships with Successive Projections