Non-convex clustering via proximal alternating linearized minimization method

Clustering is a fundamental learning task in a wide range of research fields. The most popular clustering algorithm is arguably the K-means algorithm, it is well known that the performance of K-mea...

[1]  Patricio A. Vela,et al.  A Comparative Study of Efficient Initialization Methods for the K-Means Clustering Algorithm , 2012, Expert Syst. Appl..

[2]  Jiming Peng,et al.  Advanced Optimization Laboratory Title : Approximating K-means-type clustering via semidefinite programming , 2005 .

[3]  Dorin Comaniciu,et al.  Mean Shift: A Robust Approach Toward Feature Space Analysis , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[4]  S. P. Lloyd,et al.  Least squares quantization in PCM , 1982, IEEE Trans. Inf. Theory.

[5]  Mohammed Bennamoun,et al.  Linear Regression for Face Recognition , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[6]  Yuan Yan Tang,et al.  Face Recognition Under Varying Illumination Using Gradientfaces , 2009, IEEE Transactions on Image Processing.

[7]  J. A. Hartigan,et al.  A k-means clustering algorithm , 1979 .

[8]  E. Forgy,et al.  Cluster analysis of multivariate data : efficiency versus interpretability of classifications , 1965 .

[9]  Yuan Yan Tang,et al.  Skeletonization of Ribbon-Like Shapes Based on a New Wavelet Function , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[10]  Adrian S. Lewis,et al.  Alternating Projections on Manifolds , 2008, Math. Oper. Res..

[11]  Vladlen Koltun,et al.  Robust continuous clustering , 2017, Proceedings of the National Academy of Sciences.

[12]  Pierre Hansen,et al.  NP-hardness of Euclidean sum-of-squares clustering , 2008, Machine Learning.

[13]  Yuan Yan Tang,et al.  Topology Preserving Non-negative Matrix Factorization for Face Recognition , 2008, IEEE Transactions on Image Processing.

[14]  Alan Edelman,et al.  The Geometry of Algorithms with Orthogonality Constraints , 1998, SIAM J. Matrix Anal. Appl..

[15]  Hédy Attouch,et al.  Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Lojasiewicz Inequality , 2008, Math. Oper. Res..

[16]  Yuan Yan Tang,et al.  Offline Recognition of Chinese Handwriting by Multifeature and Multilevel Classification , 1998, IEEE Trans. Pattern Anal. Mach. Intell..

[17]  Delbert Dueck,et al.  Clustering by Passing Messages Between Data Points , 2007, Science.

[18]  Yuan Yan Tang,et al.  New method for feature extraction based on fractal behavior , 2002, Pattern Recognit..

[19]  Marc Teboulle,et al.  Proximal alternating linearized minimization for nonconvex and nonsmooth problems , 2013, Mathematical Programming.

[20]  Yuan Yan Tang,et al.  Multiscale facial structure representation for face recognition under varying illumination , 2009, Pattern Recognit..

[21]  Hyeonjoon Moon,et al.  The FERET Evaluation Methodology for Face-Recognition Algorithms , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[22]  Yuan Yan Tang,et al.  Learning the Distribution Preserving Semantic Subspace for Clustering , 2017, IEEE Transactions on Image Processing.

[23]  Ulrike von Luxburg,et al.  A tutorial on spectral clustering , 2007, Stat. Comput..

[24]  David J. Kriegman,et al.  From Few to Many: Illumination Cone Models for Face Recognition under Variable Lighting and Pose , 2001, IEEE Trans. Pattern Anal. Mach. Intell..

[25]  Bin Xu,et al.  Generalized Discriminant Analysis: A Matrix Exponential Approach , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[26]  Jitendra Malik,et al.  Normalized cuts and image segmentation , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[27]  Avinash C. Kak,et al.  PCA versus LDA , 2001, IEEE Trans. Pattern Anal. Mach. Intell..

[28]  Yuan Yan Tang,et al.  Characterization of Dirac-structure edges with wavelet transform , 2000, IEEE Trans. Syst. Man Cybern. Part B.