• Publications
  • Influence
The Why and How of Nonnegative Matrix Factorization
  • N. Gillis
  • Mathematics, Computer Science
  • ArXiv
  • 21 January 2014
TLDR
Nonnegative matrix factorization (NMF) has become a widely used tool for the analysis of high-dimensional data as it automatically extracts sparse and meaningful features from a set of nonnegative data vectors. Expand
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Accelerated Multiplicative Updates and Hierarchical ALS Algorithms for Nonnegative Matrix Factorization
TLDR
We propose a simple way to significantly accelerate these schemes, based on a careful analysis of the computational cost needed at each iteration, while preserving their convergence properties. Expand
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Two algorithms for orthogonal nonnegative matrix factorization with application to clustering
TLDR
We show mathematical equivalence between ONMF and a weighted variant of spherical k-means, from which we derive a simple EM-like algorithm. Expand
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M L ] 7 O ct 2 01 3 Fast and Robust Recursive Algorithms for Separable Nonnegative Matrix Factorization ∗
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 nonnegativeExpand
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Fast and Robust Recursive Algorithmsfor Separable Nonnegative Matrix Factorization
  • N. Gillis, S. Vavasis
  • Mathematics, Computer Science
  • IEEE Transactions on Pattern Analysis and Machine…
  • 6 August 2012
TLDR
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 problemunder the linear mixing model and the pure-pixel assumption. Expand
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Using underapproximations for sparse nonnegative matrix factorization
TLDR
We introduce a novel approach to solve NMF problems, based on the use of an underapproximation technique, and show its effectiveness to obtain sparse solutions. Expand
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Low-Rank Matrix Approximation with Weights or Missing Data Is NP-Hard
TLDR
We prove that computing an optimal WLRA is NP-hard, already when a rank-one approximation is sought. Expand
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Hierarchical Clustering of Hyperspectral Images Using Rank-Two Nonnegative Matrix Factorization
TLDR
We design a fast hierarchical clustering algorithm for high-resolution hyperspectral images (HSI). Expand
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  • 9
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Nonnegative Factorization and The Maximum Edge Biclique Problem
Nonnegative matrix factorization (NMF) is a data analysis technique based on the approximation of a nonnegative matrix with a product of two nonnegative factors, which allows compression andExpand
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A Signal Processing Perspective on Hyperspectral Unmixing: Insights from Remote Sensing
TLDR
Blind hyperspectral unmixing (HU), also known as unsupervised HU, is one of the most prominent research topics in signal processing (SP, machine learning, and optimization. Expand
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