On the Geometric Interpretation of the Nonnegative Rank

[1]  V. Maroulas Probability Matrices , 2014, Encyclopedia of Social Network Analysis and Mining.

[2]  Jorge Manzi,et al.  School System Evaluation by Value Added Analysis Under Endogeneity , 2013, Psychometrika.

[3]  Andrea Silvestrini,et al.  Aggregation of exponential smoothing processes with an application to portfolio risk evaluation , 2013 .

[4]  Sanjeev Arora,et al.  Computing a nonnegative matrix factorization -- provably , 2011, STOC '12.

[5]  Nicolas Gillis,et al.  Accelerated Multiplicative Updates and Hierarchical ALS Algorithms for Nonnegative Matrix Factorization , 2011, Neural Computation.

[6]  Nicolas Gillis,et al.  A multilevel approach for nonnegative matrix factorization , 2010, J. Comput. Appl. Math..

[7]  Nathan Krislock,et al.  Euclidean Distance Matrices and Applications , 2012 .

[8]  Pierre Pestieau,et al.  The impact of a minimum pension on old age poverty and its budgetary cost. Evidence from Latin America , 2011 .

[9]  Axel Gautier,et al.  Universal Service Financing in Competitive Postal Markets: One Size Does Not Fit All , 2011 .

[10]  V. Kaibel Extended Formulations in Combinatorial Optimization , 2011, 1104.1023.

[11]  Miguel A. Carreira-Perpinan,et al.  Dimensionality Reduction , 2011 .

[12]  Nicolas Gillis,et al.  Dimensionality reduction, classification, and spectral mixture analysis using non-negative underapproximation , 2011 .

[13]  Hiroshi Uno,et al.  Nested potentials and robust equilibria , 2011 .

[14]  Volker Kaibel,et al.  Constructing Extended Formulations from Reflection Relations , 2010, IPCO.

[15]  Nicolas Gillis Nonnegative matrix factorization : complexity, algorithms and applications , 2011 .

[16]  J. Rombouts,et al.  Option Pricing with Asymmetric Heteroskedastic Normal Mixture Models , 2010 .

[17]  Matthew M Lin,et al.  On the Nonnegative Rank of Euclidean Distance Matrices. , 2010, Linear algebra and its applications.

[18]  Jean-Pierre Florens,et al.  Nonparametric frontier estimation from noisy data , 2010 .

[19]  Y. Nesterov,et al.  Double smoothing technique for infinite-dimensional optimization problems with applications to optimal control , 2010 .

[20]  Rüdiger Stephan,et al.  An extension of disjunctive programming and its impact for compact tree formulations , 2010, 1007.1136.

[21]  Thierry Bréchet,et al.  Technological greening, eco-efficiency and no-regret strategy , 2010 .

[22]  Yves Smeers,et al.  Stochastic Equilibrium Models for Generation Capacity Expansion , 2010 .

[23]  Yurii Nesterov,et al.  Solving Infinite-dimensional Optimization Problems by Polynomial Approximation , 2010 .

[24]  Tanguy Isaac,et al.  When frictions favour information revelation , 2010 .

[25]  Lars Stentoft,et al.  Multivariate Option Pricing with Time Varying Volatility and Correlations , 2010 .

[26]  Nicolas Gillis,et al.  Dimensionality reduction, classification, and spectral mixture analysis using nonnegative underapproximation , 2010, Defense + Commercial Sensing.

[27]  Elena Molis,et al.  Experimental results on the roommate problem , 2010 .

[28]  Koen Decancq,et al.  Copula-Based Orderings of Multivariate Dependence , 2010 .

[29]  Jean-Charles Lange,et al.  Design of a network of reusable logistic containers , 2010 .

[30]  Paul Belleflamme,et al.  Industrial Organization: Markets and Strategies , 2010 .

[31]  M. Jünger,et al.  50 Years of Integer Programming 1958-2008 - From the Early Years to the State-of-the-Art , 2010 .

[32]  LeRoy B. Beasley,et al.  Real rank versus nonnegative rank , 2009 .

[33]  Fabio Rapallo,et al.  Probability matrices, non-negative rank, and parameterization of mixture models , 2009, 0911.0412.

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

[35]  Stephen A. Vavasis,et al.  On the Complexity of Nonnegative Matrix Factorization , 2007, SIAM J. Optim..

[36]  Heng Tao Shen,et al.  Dimensionality Reduction , 2009, Encyclopedia of Database Systems.

[37]  Yassine Lefouili,et al.  Leniency programs for multimarket firms: The effect of Amnesty Plus on cartel formation ☆ , 2012 .

[38]  Nicolas Gillis,et al.  Nonnegative Factorization and The Maximum Edge Biclique Problem , 2008, 0810.4225.

[39]  Jacques-François Thisse,et al.  Economic Geography: The Integration of Regions and Nations , 2008 .

[40]  Moody T. Chu,et al.  Low-Dimensional Polytope Approximation and Its Applications to Nonnegative Matrix Factorization , 2008, SIAM J. Sci. Comput..

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

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

[43]  W. Pohlmeier,et al.  High frequency financial econometrics : recent developments , 2007 .

[44]  Laurence A. Wolsey,et al.  Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, 4th International Conference, CPAIOR 2007, Brussels, Belgium, May 23-26, 2007, Proceedings , 2007, CPAIOR.

[45]  Valerie L. Watts Fractional Biclique Covers and Partitions of Graphs , 2006, Electron. J. Comb..

[46]  J. Gabszewicz La différenciation des produits , 2006 .

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

[48]  R. Amir Supermodularity and Complementarity in Economics: An Elementary Survey , 2003 .

[49]  René Peeters,et al.  The maximum edge biclique problem is NP-complete , 2003, Discret. Appl. Math..

[50]  Daniel Bienstock,et al.  Potential Function Methods for Approximately Solving Linear Programming Problems: Theory and Practice , 2002 .

[51]  Arkadi Nemirovski,et al.  On Polyhedral Approximations of the Second-Order Cone , 2001, Math. Oper. Res..

[52]  James Renegar,et al.  A mathematical view of interior-point methods in convex optimization , 2001, MPS-SIAM series on optimization.

[53]  J. Huriot,et al.  Economics of Cities , 2000 .

[54]  F. Glineur Computational Experiments With a Linear Approximation of Second-Order Cone Optimization , 2000 .

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

[56]  Chein-I Chang,et al.  Multispectral and hyperspectral image analysis with convex cones , 1999, IEEE Trans. Geosci. Remote. Sens..

[57]  D. M. Topkis Supermodularity and Complementarity , 1998 .

[58]  Michael T. Goodrich,et al.  On the Complexity of Optimization Problems for 3-dimensional Convex Polyhedra and Decision Trees , 1997, Comput. Geom..

[59]  Ramaswamy Chandrasekaran,et al.  Finding the Set of All Minimal Nested Convex Polygons , 1996, CCCG.

[60]  Christian Gourieroux,et al.  Simulation-based econometric methods , 1996 .

[61]  G. Ziegler Lectures on Polytopes , 1994 .

[62]  J. Boardman,et al.  Geometric mixture analysis of imaging spectrometry data , 1994, Proceedings of IGARSS '94 - 1994 IEEE International Geoscience and Remote Sensing Symposium.

[63]  Maurice D. Craig,et al.  Minimum-volume transforms for remotely sensed data , 1994, IEEE Trans. Geosci. Remote. Sens..

[64]  Joel E. Cohen,et al.  Nonnegative ranks, decompositions, and factorizations of nonnegative matrices , 1993 .

[65]  Kenneth L. Clarkson,et al.  Algorithms for Polytope Covering and Approximation , 1993, WADS.

[66]  Peter L. Jackson,et al.  On the convexity of a function related to the Wagner-Whitin model , 1992, Oper. Res. Lett..

[67]  Joseph S. B. Mitchell,et al.  Separation and approximation of polyhedral surfaces , 1991 .

[68]  Cao An Wang Finding minimal nested polygons , 1991, BIT Comput. Sci. Sect..

[69]  安藤 毅 Completely positive matrices , 1991 .

[70]  G. Das,et al.  Approximation schemes in computational geometry , 1990 .

[71]  Mihalis Yannakakis,et al.  Expressing combinatorial optimization problems by linear programs , 1991, STOC '88.

[72]  Alok Aggarwal,et al.  Finding minimal convex nested polygons , 1985, SCG '85.

[73]  Zvi Galil,et al.  Lower bounds on communication complexity , 1984, STOC '84.

[74]  Michiel Hazewinkel On positive vectors, positive matrices and the specialization order , 1984 .

[75]  J. Orlin Contentment in graph theory: Covering graphs with cliques , 1977 .

[76]  L. B. Thomas Rank Factorization of Nonnegative Matrices (A. Berman) , 1974 .

[77]  A. Berman Rank Factorization of Nonnegative Matrices , 1973 .