SVD Based Graph Regularized Matrix Factorization

Graph regularized matrix factorization has been proposed by Cai et al. 2011 with an alternate optimization strategy due to the difficulty of close form solution. In this paper, we develop a novel method for graph regularized matrix factorization. This method is based on Singular Value Decomposition SVD, and its solution is close formed. We carried out experiments on a database for the task of clustering problem to shown the advantage of the proposed method.

[1]  Per Ola Börjesson,et al.  OFDM channel estimation by singular value decomposition , 1996, Proceedings of Vehicular Technology Conference - VTC.

[2]  Zhang Xiaodong,et al.  A new upper bound for eigenvalues of the laplacian matrix of a graph , 1997 .

[3]  Pablo Tamayo,et al.  Metagenes and molecular pattern discovery using matrix factorization , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[4]  Zheng Hong,et al.  Non-Negative Matrix Factorization Based on Double Sparsity K-SVD , 2012 .

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

[6]  Christos Boutsidis,et al.  SVD based initialization: A head start for nonnegative matrix factorization , 2008, Pattern Recognit..

[7]  Dejan Plavsic,et al.  The Laplacian matrix in chemistry , 1994, J. Chem. Inf. Comput. Sci..

[8]  Jim Jing-Yan Wang,et al.  Multiple graph regularized nonnegative matrix factorization , 2013, Pattern Recognit..

[9]  Abderrahim Elmoataz,et al.  Graph regularization for color image processing , 2007, Comput. Vis. Image Underst..

[10]  Dewen Hu,et al.  Comment on: "Two-dimensional locality preserving projections (2DLPP) with its application to palmprint recognition" , 2008, Pattern Recognit..

[11]  D. Botstein,et al.  Singular value decomposition for genome-wide expression data processing and modeling. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[12]  Yves Kamp,et al.  A Frobenius norm approach to glottal closure detection from the speech signal , 1994, IEEE Trans. Speech Audio Process..

[13]  Xuan Li,et al.  Cluster Ensembles via Weighted Graph Regularized Nonnegative Matrix Factorization , 2011, ADMA.

[14]  Joos Vandewalle,et al.  A Multilinear Singular Value Decomposition , 2000, SIAM J. Matrix Anal. Appl..

[15]  C. Fung,et al.  Multi-response optimization in friction properties of PBT composites using Taguchi method and principle component analysis , 2005 .

[16]  Yulian Zhu,et al.  Subpattern-based principle component analysis , 2004, Pattern Recognit..

[17]  R. Ocampo-Pérez,et al.  Adsorption of Fluoride from Water Solution on Bone Char , 2007 .

[18]  Tuomas Virtanen,et al.  Monaural Sound Source Separation by Nonnegative Matrix Factorization With Temporal Continuity and Sparseness Criteria , 2007, IEEE Transactions on Audio, Speech, and Language Processing.

[19]  Bruno Carpentieri,et al.  Sparse pattern selection strategies for robust Frobenius-norm minimization preconditioners in electromagnetism , 2000 .

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

[21]  Christopher M. Bishop,et al.  A Hierarchical Latent Variable Model for Data Visualization , 1998, IEEE Trans. Pattern Anal. Mach. Intell..

[22]  Michael Elad,et al.  Compression of facial images using the K-SVD algorithm , 2008, J. Vis. Commun. Image Represent..

[23]  Kilian Q. Weinberger,et al.  Graph Laplacian Regularization for Large-Scale Semidefinite Programming , 2006, NIPS.

[24]  Xiaolei Wang,et al.  Non-negative matrix factorization by maximizing correntropy for cancer clustering , 2013, BMC Bioinformatics.

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

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

[27]  Lei Wang,et al.  Linear Projective Non-Negative Matrix Factorization , 2013 .

[28]  Xin Gao,et al.  Adaptive graph regularized Nonnegative Matrix Factorization via feature selection , 2012, Proceedings of the 21st International Conference on Pattern Recognition (ICPR2012).

[29]  Tong Zhang,et al.  Linear prediction models with graph regularization for web-page categorization , 2006, KDD '06.

[30]  Zilan Hu,et al.  Comment on: "Two-dimensional locality preserving projections (2DLPP) with its application to palmprint recognition" , 2008, Pattern Recognit..

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

[32]  Bin Luo,et al.  2D-LPP: A two-dimensional extension of locality preserving projections , 2007, Neurocomputing.

[33]  Xiaolong Teng,et al.  Face recognition using discriminant locality preserving projections , 2006, Image Vis. Comput..

[34]  R. Merris.  Laplacian matrices of graphs: a survey , 1994 .

[35]  Jeng-Shyang Pan,et al.  Kernel class-wise locality preserving projection , 2008, Inf. Sci..

[36]  Thomas S. Huang,et al.  Graph Regularized Nonnegative Matrix Factorization for Data Representation. , 2011, IEEE transactions on pattern analysis and machine intelligence.

[37]  Jing Liu,et al.  Structure preserving non-negative matrix factorization for dimensionality reduction , 2013, Comput. Vis. Image Underst..

[38]  M. Elad,et al.  $rm K$-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation , 2006, IEEE Transactions on Signal Processing.

[39]  Michael Elad,et al.  K-SVD and its non-negative variant for dictionary design , 2005, SPIE Optics + Photonics.

[40]  S. Zhao,et al.  Monitoring of Processes with Multiple Operating Modes through Multiple Principle Component Analysis Models , 2004 .

[41]  Mahdi Khodadadzadeh,et al.  Graph Regularized Nonnegative Matrix Factorization for Hyperspectral Data Unmixing , 2011, 2011 7th Iranian Conference on Machine Vision and Image Processing.

[42]  Paulo J. G. Lisboa,et al.  Discriminant Convex Non-negative Matrix Factorization for the classification of human brain tumours , 2013, Pattern Recognit. Lett..