Journal ArticleDOI
Least squares formulation of robust non-negative factor analysis
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TLDR
Positive matrix factorization (PMF) is a recently published factor analytic technique where the left and right factor matrices (corresponding to scores and loadings) are constrained to non-negative values as mentioned in this paper.About:
This article is published in Chemometrics and Intelligent Laboratory Systems.The article was published on 1997-05-01. It has received 1734 citations till now. The article focuses on the topics: Least squares & Nonnegative matrix.read more
Citations
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Journal ArticleDOI
Learning the parts of objects by non-negative matrix factorization
TL;DR: An algorithm for non-negative matrix factorization is demonstrated that is able to learn parts of faces and semantic features of text and is in contrast to other methods that learn holistic, not parts-based, representations.
Learning parts of objects by non-negative matrix factorization
TL;DR: In this article, non-negative matrix factorization is used to learn parts of faces and semantic features of text, which is in contrast to principal components analysis and vector quantization that learn holistic, not parts-based, representations.
Proceedings Article
Algorithms for Non-negative Matrix Factorization
Daniel D. Lee,H. Sebastian Seung +1 more
TL;DR: Two different multiplicative algorithms for non-negative matrix factorization are analyzed and one algorithm can be shown to minimize the conventional least squares error while the other minimizes the generalized Kullback-Leibler divergence.
Journal ArticleDOI
Bounding the role of black carbon in the climate system: A scientific assessment
Tami C. Bond,Sarah J. Doherty,David W. Fahey,Piers M. Forster,Terje Koren Berntsen,Benjamin DeAngelo,Mark Flanner,Steven J. Ghan,Bernd Kärcher,Dorothy Koch,Stefan Kinne,Yutaka Kondo,Patricia K. Quinn,Marcus C. Sarofim,Martin G. Schultz,Michael Schulz,Chandra Venkataraman,Hua Zhang,Shiqiu Zhang,Nicolas Bellouin,Sarath K. Guttikunda,Philip K. Hopke,Mark Z. Jacobson,Johannes W. Kaiser,Zbigniew Klimont,Ulrike Lohmann,Joshua P. Schwarz,Drew Shindell,Trude Storelvmo,Stephen G. Warren,Charles S. Zender +30 more
TL;DR: In this paper, the authors provided an assessment of black-carbon climate forcing that is comprehensive in its inclusion of all known and relevant processes and that is quantitative in providing best estimates and uncertainties of the main forcing terms: direct solar absorption; influence on liquid, mixed phase, and ice clouds; and deposition on snow and ice.
Book
Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation
TL;DR: This book provides a broad survey of models and efficient algorithms for Nonnegative Matrix Factorization (NMF), including NMFs various extensions and modifications, especially Nonnegative Tensor Factorizations (NTF) and Nonnegative Tucker Decompositions (NTD).
References
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Journal ArticleDOI
Robust Estimation of a Location Parameter
TL;DR: In this article, a new approach toward a theory of robust estimation is presented, which treats in detail the asymptotic theory of estimating a location parameter for contaminated normal distributions, and exhibits estimators that are asyptotically most robust (in a sense to be specified) among all translation invariant estimators.
Journal ArticleDOI
Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values†
Pentti Paatero,Unto Tapper +1 more
TL;DR: In this paper, a new variant of Factor Analysis (PMF) is described, where the problem is solved in the weighted least squares sense: G and F are determined so that the Frobenius norm of E divided (element-by-element) by σ is minimized.
Journal ArticleDOI
Tensorial resolution: A direct trilinear decomposition
TL;DR: In this article, the authors introduced a method for reducing the problem to a rectangular generalized eigenvalue-eigenvector equation where the eigenvectors are the contravariant form (pseudo-inverse) of the actual factors.
Journal ArticleDOI
Analysis of different modes of factor analysis as least squares fit problems
Pentti Paatero,Unto Tapper +1 more
TL;DR: It is shown that each mode of principal component analysis or ‘factor analysis’ is equivalent to solving a certain least squares problem where certain error estimators σ ij are assumed for the measured data matrix X ij and the best posssible scaling and a near-optimal scaling are introduced.
Journal ArticleDOI
Source identification of bulk wet deposition in Finland by positive matrix factorization
TL;DR: In this paper, a positive matrix factorization (PMF) was applied to a Finnish data set (18 years, 15 locations) of monthly bulk wet deposition concentrations of strong acids, SO4, NO3, NH4, total nitrogen (Ntot), total phosphorus (Ptot) and total organic carbon (TOC).
Related Papers (5)
Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values†
Pentti Paatero,Unto Tapper +1 more