Fetching the paper…
Reading the bibliography…
Nonnegative matrix factorizations are often encountered in data mining applications where they are used to explain datasets by a small number of parts.
Expressing combinatorial optimization problems by linear programs
Mihalis Yannakakis · 1902
Earlier work this paper cites.
The rigidity of graphs, II
Leonard Asimow and Ben Roth · 1979
Earlier work this paper cites.
Nonnegative ranks, decompositions, and factorizations of nonnegative matrices
Joel E. Cohen and Uriel G. Rothblum · 1993
Earlier work this paper cites.
Learning the parts of objects by non-negative matrix factorization
Daniel D. Lee and Sebastian H. Seung · 1999
Earlier work this paper cites.
polymake: a framework for analyzing convex polytopes
Ewgenij Gawrilow and Michael Joswig · 2000
Earlier work this paper cites.
Completely positive matrices
Berman Abraham and Shaked-Monderer Naomi · 2003
Earlier work this paper cites.
Stochastic factorizations, sandwiched simplices and the topology of the space of explanations
David Mond, Jim Smith, and Duco van Straten · 2003
Earlier work this paper cites.
Non-negative matrix factorization for polyphonic music transcription
Paris Smaragdis and Judith C. Brown · 2003
Earlier work this paper cites.
Document clustering based on non-negative matrix factorization
Wei Xu, Xin Liu, and Yihong Gong · 2003
Earlier work this paper cites.
When does non-negative matrix factorization give a correct decomposition into parts?
David Donoho and Victoria Stodden · 2004
Earlier work this paper cites.
First results on uniqueness of sparse non-negative matrix factorization
Fabian J. Theis, Kurt Stadlthanner, and Toshihisa Tanaka · 2005
Earlier work this paper cites.
Orthogonal nonnegative matrix t-factorizations for clustering
Chris Ding, Tao Li, Wei Peng, and Haesun Park · 2006
Cited alongside, same era.
Nonnegative matrix factorization for spectral data analysis
V. Paul Pauca, Jon Piper, and Robert J. Plemmons · 2006
Cited alongside, same era.
Nonnegative matrix factorization: An analytical and interpretive tool in computational biology
Karthik Devarajan · 2008
Cited alongside, same era.
Theorems on positive data: On the uniqueness of NMF
Hans Laurberg, Mads Græsbøll Christensen, Mark D. Plumbley, Lars Kai Hansen, and Søren Holdt Jensen · 2008
Cited alongside, same era.
A convex analysis-based minimum-volume enclosing simplex algorithm for hyperspectral unmixing
Tsung-Han Chan, Chong-Yung Chi, Yu-Min Huang, and Wing-Kin Ma · 2009
Cited alongside, same era.
Nonnegative matrix and tensor factorizations: Applications to exploratory multi-way data analysis and blind source separation
On the geometric interpretation of the nonnegative rank
Nicolas Gillis and François Glineur · 2012
Later among the works it cites.
Blind separation of quasi-stationary sources: Exploiting convex geometry in covariance domain
Xiao Fu, Wing-Kin Ma, Kejun Huang, and Nicholas D. Sidiropoulos · 2015
Later among the works it cites.
Fixed points of the EM algorithm and nonnegative rank boundaries
Kaie Kubjas, Elina Robeva, and Bernd Sturmfels · 2015
Later among the works it cites.
Identifiability of the simplex volume minimization criterion for blind hyperspectral unmixing: The no-pure-pixel case
Chia-Hsiang Lin, Wing-Kin Ma, Wei-Chiang Li, Chong-Yung Chi, and ArulMurugan Ambikapathi · 2015
Later among the works it cites.
An almost optimal algorithm for computing nonnegative rank
Ankur Moitra · 2016
Later among the works it cites.
Heuristics for exact nonnegative matrix factorization
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Andrzej Cichocki, Rafal Zdunek, Anh Huy Phan, and Shun-ichi Amari · 2009
Cited alongside, same era.
On the complexity of nonnegative matrix factorization
Stephen A. Vavasis · 2009
Cited alongside, same era.
Nonnegative least-correlated component analysis for separation of dependent sources by volume maximization
Fa-Yu Wang, Chong-Yung Chi, Tsung-Han Chan, and Yue Wang · 2009
Cited alongside, same era.
Uniqueness of low-rank matrix completion by rigidity theory
Amit Singer and Mihai Cucuringu · 2010
Cited alongside, same era.
Sparse and unique nonnegative matrix factorization through data preprocessing
Nicolas Gillis · 2012
Cited alongside, same era.
Normaliz. Algorithms for rational cones and affine monoids
Winfried Bruns, Bogdan Ichim, Tim Römer, Richard Sieg, and Christof Söger
Cited in the paper.
Macaulay2, a software system for research in algebraic geometry
Daniel R. Grayson and Michael E. Stillman
Cited in the paper.
Arnaud Vandaele, Nicolas Gillis, François Glineur, and Daniel Tuyttens · 2016
Later among the works it cites.
On identifiability of nonnegative matrix factorization
Xiao Fu, Kejun Huang, and Nicholas D. Sidiropoulos · 2018
Later among the works it cites.
Infinitesimally rigid factorizations of nonnegative rank four
Huanhuan Chen · 2019
Closest in time.
Nonnegative matrix factorization for signal and data analytics: Identifiability, algorithms, and applications
Xiao Fu, Kejun Huang, Nicholas D. Sidiropoulos, and Wing-Kin Ma · 2019
Closest in time.
Nonnegative rank depends on the field
Yaroslav Shitov · 2019
Closest in time.