• Publications
  • Influence
The Why and How of Nonnegative Matrix Factorization
A recent subclass of NMF problems is presented, referred to as near-separable NMF, that can be solved efficiently (that is, in polynomial time), even in the presence of noise.
Accelerated Multiplicative Updates and Hierarchical ALS Algorithms for Nonnegative Matrix Factorization
A simple way to significantly accelerate two well-known algorithms designed to solve NMF problems: the multiplicative updates of Lee and Seung and the hierarchical alternating least squares of Cichocki et al. is proposed.
Fast and Robust Recursive Algorithmsfor Separable Nonnegative Matrix Factorization
  • Nicolas Gillis, S. Vavasis
  • Computer Science, Mathematics
    IEEE Transactions on Pattern Analysis and Machine…
  • 6 August 2012
This paper presents a family of fast recursive algorithms that are equivalent to the hyperspectral unmixing problem under the linear mixing model and the pure-pixel assumption and proves they are robust under any small perturbations of the input data matrix.
A Signal Processing Perspective on Hyperspectral Unmixing: Insights from Remote Sensing
The present development of blind HU seems to be converging to a point where the lines between remote sensing-originated ideas and advanced SP and optimization concepts are no longer clear, and insights from both sides would be used to establish better methods.
Low-Rank Matrix Approximation with Weights or Missing Data Is NP-Hard
This paper proves that computing an optimal WLRA is NP-hard, already when a rank-one approximation is sought, and shows that it is hard to compute approximate solutions to the WL RA problem with some prescribed accuracy.
Hierarchical Clustering of Hyperspectral Images Using Rank-Two Nonnegative Matrix Factorization
A new rank-two nonnegative matrix factorization (NMF) algorithm is used to split the clusters, which is motivated by convex geometry concepts and is shown to outperform standard clustering techniques such as k-means, spherical k-Means, and standard NMF.
Robust near-separable nonnegative matrix factorization using linear optimization
This paper generalizes Hottopixx and proposes a new LP model which does not require normalization and detects the factorization rank automatically, which is more flexible, significantly more tolerant to noise, and can easily be adapted to handle outliers and other noise models.
Semidefinite Programming Based Preconditioning for More Robust Near-Separable Nonnegative Matrix Factorization
A preconditioning based on the minimum volume ellipsoid and semidefinite programming making the input matrix well-conditioned can improve significantly the performance of near-separable NMF algorithms which is illustrated on the popular successive projection algorithm (SPA).