Sparse non-negative matrix factorizations via alternating non-negativity-constrained least squares for microarray data analysis
Hyun-Chul Kim,Haesun Park +1 more
TLDR
The experimental results illustrate that the proposed sparse NMF algorithm often achieves better clustering performance with shorter computing time compared to other existing NMF algorithms.Abstract:
Motivation: Many practical pattern recognition problems require non-negativity constraints. For example, pixels in digital images and chemical concentrations in bioinformatics are non-negative. Sparse non-negative matrix factorizations (NMFs) are useful when the degree of sparseness in the non-negative basis matrix or the non-negative coefficient matrix in an NMF needs to be controlled in approximating high-dimensional data in a lower dimensional space.
Results: In this article, we introduce a novel formulation of sparse NMF and show how the new formulation leads to a convergent sparse NMF algorithm via alternating non-negativity-constrained least squares. We apply our sparse NMF algorithm to cancer-class discovery and gene expression data analysis and offer biological analysis of the results obtained. Our experimental results illustrate that the proposed sparse NMF algorithm often achieves better clustering performance with shorter computing time compared to other existing NMF algorithms.
Availability: The software is available as supplementary material.
Contact:hskim@cc.gatech.edu, hpark@acc.gatech.edu
Supplementary information: Supplementary data are available at Bioinformatics online.read more
Citations
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Journal ArticleDOI
Convex and Semi-Nonnegative Matrix Factorizations
TL;DR: This work considers factorizations of the form X = FGT, and focuses on algorithms in which G is restricted to containing nonnegative entries, but allowing the data matrix X to have mixed signs, thus extending the applicable range of NMF methods.
Journal ArticleDOI
A flexible R package for nonnegative matrix factorization
Renaud Gaujoux,Cathal Seoighe +1 more
TL;DR: The NMF package helps realize the potential of Nonnegative Matrix Factorization, especially in bioinformatics, providing easy access to methods that have already yielded new insights in many applications and facilitating the combination of these to produce new NMF strategies.
Journal ArticleDOI
Nonnegative Matrix Factorization: A Comprehensive Review
Yu-Xiong Wang,Yu-Jin Zhang +1 more
TL;DR: A comprehensive survey of NMF algorithms can be found in this paper, where the principles, basic models, properties, and algorithms along with its various modifications, extensions, and generalizations are summarized systematically.
Journal ArticleDOI
On the Complexity of Nonnegative Matrix Factorization
TL;DR: An exact version of nonnegative matrix factorization is defined and it is established that it is equivalent to a problem in polyhedral combinatorics; it is NP-hard; and that a polynomial-time local search heuristic exists.
Journal ArticleDOI
Fast and efficient estimation of individual ancestry coefficients.
Eric Frichot,François Mathieu,Théo Trouillon,Théo Trouillon,Guillaume Bouchard,Olivier François +5 more
TL;DR: This work presents a fast and efficient method for estimating individual ancestry coefficients based on sparse nonnegative matrix factorization algorithms in the computer program sNMF and applied it to human and plant data sets.
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