Non-negative mixtures

This is the author's accepted pre-print of the article, first published as M. D. Plumbley, A. Cichocki and R. Bro. Non-negative mixtures. In P. Comon and C. Jutten (Ed), Handbook of Blind Source Separation: Independent Component Analysis and Applications. Chapter 13, pp. 515-547. Academic Press, Feb 2010. ISBN 978-0-12-374726-6 DOI: 10.1016/B978-0-12-374726-6.00018-7

[1]  G. Buchsbaum,et al.  Color categories revealed by non-negative matrix factorization of Munsell color spectra , 2002, Vision Research.

[2]  Max Welling,et al.  Positive tensor factorization , 2001, Pattern Recognit. Lett..

[3]  Andrzej Cichocki,et al.  Novel Multi-layer Non-negative Tensor Factorization with Sparsity Constraints , 2007, ICANNGA.

[4]  Romà Tauler,et al.  Self-modelling curve resolution in studies of spectrometric titrations of multi-equilibria systems by factor analysis , 1991 .

[5]  Kazuyoshi Itoh,et al.  Blind signal separation by algebraic independent component analysis , 2000, LEOS 2000. 2000 IEEE Annual Meeting Conference Proceedings. 13th Annual Meeting. IEEE Lasers and Electro-Optics Society 2000 Annual Meeting (Cat. No.00CH37080).

[6]  S. Amari,et al.  Nonnegative Matrix and Tensor Factorization [Lecture Notes] , 2008, IEEE Signal Processing Magazine.

[7]  D. Donoho,et al.  Sparse MRI: The application of compressed sensing for rapid MR imaging , 2007, Magnetic resonance in medicine.

[8]  D Charles,et al.  Modelling multiple-cause structure using rectification constraints. , 1998, Network.

[9]  Paris Smaragdis,et al.  Convolutive Speech Bases and Their Application to Supervised Speech Separation , 2007, IEEE Transactions on Audio, Speech, and Language Processing.

[10]  R. Bro PARAFAC. Tutorial and applications , 1997 .

[11]  R W Prager,et al.  Development of low entropy coding in a recurrent network. , 1996, Network.

[12]  Mark D. Plumbley Algorithms for nonnegative independent component analysis , 2003, IEEE Trans. Neural Networks.

[13]  Xin Liu,et al.  Document clustering based on non-negative matrix factorization , 2003, SIGIR.

[14]  George Francis Harpur,et al.  Low Entropy Coding with Unsupervised Neural Networks , 1997 .

[15]  Bruce R. Kowalski,et al.  An extension of the multivariate component-resolution method to three components , 1985 .

[16]  Chris H. Q. Ding,et al.  Convex and Semi-Nonnegative Matrix Factorizations , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[17]  E. Oja,et al.  On stochastic approximation of the eigenvectors and eigenvalues of the expectation of a random matrix , 1985 .

[18]  Patrik O. Hoyer,et al.  Non-negative sparse coding , 2002, Proceedings of the 12th IEEE Workshop on Neural Networks for Signal Processing.

[19]  Tamara G. Kolda,et al.  Tensor Decompositions and Applications , 2009, SIAM Rev..

[20]  R. Plemmons,et al.  Optimality, computation, and interpretation of nonnegative matrix factorizations , 2004 .

[21]  Derry Fitzgerald,et al.  Extended Nonnegative Tensor Factorisation Models for Musical Sound Source Separation , 2008, Comput. Intell. Neurosci..

[22]  H. Sebastian Seung,et al.  Learning the parts of objects by non-negative matrix factorization , 1999, Nature.

[23]  P. Foldiak,et al.  Adaptive network for optimal linear feature extraction , 1989, International 1989 Joint Conference on Neural Networks.

[24]  Daniel D. Lee,et al.  APPLICATION OF NON-NEGATIVE MATRIX FACTORIZATION TO DYNAMIC POSITRON EMISSION TOMOGRAPHY , 2001 .

[25]  D. J. Leggett,et al.  Numerical analysis of multicomponent spectra , 1977 .

[26]  Kazuyoshi Itoh,et al.  Independent component analysis by transforming a scatter diagram of mixtures of signals , 2000 .

[27]  Alberto Prieto,et al.  A neural learning algorithm for blind separation of sources based on geometric properties , 1998, Signal Process..

[28]  Lei Xu,et al.  Least mean square error reconstruction principle for self-organizing neural-nets , 1993, Neural Networks.

[29]  H. Law Research methods for multimode data analysis , 1984 .

[30]  Inderjit S. Dhillon,et al.  Fast Newton-type Methods for the Least Squares Nonnegative Matrix Approximation Problem , 2007, SDM.

[31]  Andreas Ziehe,et al.  Unmixing Hyperspectral Data , 1999, NIPS.

[32]  H. Sebastian Seung,et al.  Algorithms for Non-negative Matrix Factorization , 2000, NIPS.

[33]  Erkki Oja,et al.  Neural Networks, Principal Components, and Subspaces , 1989, Int. J. Neural Syst..

[34]  R. Henry History and fundamentals of multivariate air quality receptor models , 1997 .

[35]  R. Bro Review on Multiway Analysis in Chemistry—2000–2005 , 2006 .

[36]  Pando G. Georgiev,et al.  Blind Source Separation Algorithms with Matrix Constraints , 2003, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[37]  Mark D. Plumbley Geometrical methods for non-negative ICA: Manifolds, Lie groups and toral subalgebras , 2005, Neurocomputing.

[38]  J. Kruskal Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics , 1977 .

[39]  P. Paatero,et al.  Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values† , 1994 .

[40]  Erkki Oja,et al.  The nonlinear PCA learning rule in independent component analysis , 1997, Neurocomputing.

[41]  Victoria Stodden,et al.  When Does Non-Negative Matrix Factorization Give a Correct Decomposition into Parts? , 2003, NIPS.

[42]  Juha Karhunen,et al.  Representation and separation of signals using nonlinear PCA type learning , 1994, Neural Networks.

[43]  Richard J. Mammone,et al.  Use of non-negative matrix factorization for language model adaptation in a lecture transcription task , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).

[44]  Mark D. Plumbley ADAPTIVE LATERAL INHIBITION FOR NON-NEGATIVE ICA , 2001 .

[45]  J. Carroll,et al.  Fitting of the Latent Class model via iteratively reweighted least squares CANDECOMP with nonnegativity constraints , 1989 .

[46]  Chih-Jen Lin,et al.  Projected Gradient Methods for Nonnegative Matrix Factorization , 2007, Neural Computation.

[47]  Zhaoshui He,et al.  Extended SMART Algorithms for Non-negative Matrix Factorization , 2006, ICAISC.

[48]  Ewert Bengtsson,et al.  Using feature-vector based analysis, based on principal component analysis and independent component analysis, for analysing hyperspectral images , 2001, Proceedings 11th International Conference on Image Analysis and Processing.

[49]  R. Bro,et al.  PARAFAC2—Part I. A direct fitting algorithm for the PARAFAC2 model , 1999 .

[50]  Andrzej Cichocki,et al.  Nonnegative Tucker decomposition with alpha-divergence , 2008, 2008 IEEE International Conference on Acoustics, Speech and Signal Processing.

[51]  Tuomas Virtanen,et al.  Sound Source Separation Using Sparse Coding with Temporal Continuity Objective , 2003, ICMC.

[52]  Carlos G. Puntonet,et al.  Neural net approach for blind separation of sources based on geometric properties , 1998, Neurocomputing.

[53]  Paris Smaragdis,et al.  Non-negative Matrix Factor Deconvolution; Extraction of Multiple Sound Sources from Monophonic Inputs , 2004, ICA.

[54]  Mikkel N. Schmidt,et al.  Nonnegative Matrix Factorization with Gaussian Process Priors , 2008, Comput. Intell. Neurosci..

[55]  Morten Mørup,et al.  Nonnegative Matrix Factor 2-D Deconvolution for Blind Single Channel Source Separation , 2006, ICA.

[56]  Charles L. Lawson,et al.  Solving least squares problems , 1976, Classics in applied mathematics.

[57]  Mark D. Plumbley Conditions for nonnegative independent component analysis , 2002, IEEE Signal Processing Letters.

[58]  S. Sra Nonnegative Matrix Approximation: Algorithms and Applications , 2006 .

[59]  Rasmus Bro,et al.  MULTI-WAY ANALYSIS IN THE FOOD INDUSTRY Models, Algorithms & Applications , 1998 .

[60]  A. Cichocki,et al.  Flexible HALS algorithms for sparse non-negative matrix/tensor factorization , 2008, 2008 IEEE Workshop on Machine Learning for Signal Processing.

[61]  Michael W. Berry,et al.  Text Mining Using Non-Negative Matrix Factorizations , 2004, SDM.

[62]  Lars Kai Hansen,et al.  Algorithms for Sparse Nonnegative Tucker Decompositions , 2008, Neural Computation.

[63]  SIGIR 2003: Proceedings of the 26th Annual International ACM SIGIR Conference on Research and Development in Information Retrieval, July 28 - August 1, 2003, Toronto, Canada , 2003, SIGIR.

[64]  Ronald C. Henry,et al.  Multivariate receptor models—current practice and future trends , 2002 .

[65]  R. Henry Receptor Model Applied to Patterns in Space (RMAPS) , 1997 .

[66]  P. Földiák,et al.  Forming sparse representations by local anti-Hebbian learning , 1990, Biological Cybernetics.

[67]  Shun-ichi Amari,et al.  Blind Separation of a Mixture of Uniformly Distributed Source Signals: A Novel Approach , 1999, Neural Computation.

[68]  Andrzej Cichocki,et al.  Fast Local Algorithms for Large Scale Nonnegative Matrix and Tensor Factorizations , 2009, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[69]  Karthik Devarajan,et al.  Nonnegative Matrix Factorization: An Analytical and Interpretive Tool in Computational Biology , 2008, PLoS Comput. Biol..

[70]  Erkki Oja,et al.  A "nonnegative PCA" algorithm for independent component analysis , 2004, IEEE Transactions on Neural Networks.

[71]  Andrzej Cichocki,et al.  Fast and Efficient Algorithms for Nonnegative Tucker Decomposition , 2008, ISNN.

[72]  A. Hyvärinen,et al.  A multi-layer sparse coding network learns contour coding from natural images , 2002, Vision Research.

[73]  James Curry,et al.  Non-negative matrix factorization: Ill-posedness and a geometric algorithm , 2009, Pattern Recognit..

[74]  M. Lennon,et al.  Independent component analysis as a tool for the dimensionality reduction and the representation of hyperspectral images , 2001, IGARSS 2001. Scanning the Present and Resolving the Future. Proceedings. IEEE 2001 International Geoscience and Remote Sensing Symposium (Cat. No.01CH37217).

[75]  Tuomas Virtanen,et al.  Separation of sound sources by convolutive sparse coding , 2004, SAPA@INTERSPEECH.

[76]  Chris H. Q. Ding,et al.  Orthogonal nonnegative matrix t-factorizations for clustering , 2006, KDD '06.

[77]  R. Henry Multivariate receptor modeling by N-dimensional edge detection , 2003 .

[78]  R. Bro,et al.  A fast non‐negativity‐constrained least squares algorithm , 1997 .

[79]  Heiko Wersing,et al.  Sparse Coding with Invariance Constraints , 2003, ICANN.

[80]  Age K. Smilde,et al.  Constrained three‐mode factor analysis as a tool for parameter estimation with second‐order instrumental data , 1998 .

[81]  Seungjin Choi,et al.  Nonnegative Tucker Decomposition , 2007, 2007 IEEE Conference on Computer Vision and Pattern Recognition.

[82]  Kurt Hornik,et al.  Convergence analysis of local feature extraction algorithms , 1992, Neural Networks.

[83]  Christian Jutten,et al.  A Geometrical algorithm for blind separation of sources , 1995 .

[84]  Dietrich Lehmann,et al.  Nonsmooth nonnegative matrix factorization (nsNMF) , 2006, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[85]  P. Paatero Least squares formulation of robust non-negative factor analysis , 1997 .

[86]  Jan H. van Schuppen,et al.  Positive matrix factorization via extremal polyhedral cones , 1999 .

[87]  David J. Field,et al.  Emergence of simple-cell receptive field properties by learning a sparse code for natural images , 1996, Nature.

[88]  Andrzej Cichocki,et al.  Hierarchical ALS Algorithms for Nonnegative Matrix and 3D Tensor Factorization , 2007, ICA.

[89]  C. Lawson,et al.  Solving least squares problems , 1976, Classics in applied mathematics.

[90]  Kenji Kita,et al.  Dimensionality reduction using non-negative matrix factorization for information retrieval , 2001, 2001 IEEE International Conference on Systems, Man and Cybernetics. e-Systems and e-Man for Cybernetics in Cyberspace (Cat.No.01CH37236).

[91]  Michael W. Berry,et al.  Algorithms and applications for approximate nonnegative matrix factorization , 2007, Comput. Stat. Data Anal..

[92]  A. Cichocki,et al.  Multilayer nonnegative matrix factorisation , 2006 .

[93]  Patrik O. Hoyer,et al.  Non-negative Matrix Factorization with Sparseness Constraints , 2004, J. Mach. Learn. Res..

[94]  Yin Zhang,et al.  Accelerating the Lee-Seung Algorithm for Nonnegative Matrix Factorization , 2005 .

[95]  A. Cichocki,et al.  Nonnegative Matrix Factorization with Temporal Smoothness and / or Spatial Decorrelation Constraints , 2005 .

[96]  V. P. Pauca,et al.  Object Characterization from Spectral Data Using Nonnegative Factorization and Information Theory , 2004 .

[97]  Michael W. Spratling,et al.  Pre-synaptic lateral inhibition provides a better architecture for self-organizing neural networks. , 1999, Network.