Regularized l1-Graph for Data Clustering

l1-Graph has been proven to be effective in data clustering, which partitions the data space by using the sparse representation of the data as the similarity measure. However, the sparse representation is performed for each datum independently without taking into account the geometric structure of the data. Motivated by l1-Graph and manifold leaning, we propose Regularized l1-Graph (Rl1-Graph) for data clustering. Compared to l1-Graph, the sparse representations of Rl1-Graph are regularized by the geometric information of the data. In accordance with the manifold assumption, the sparse representations vary smoothly along the geodesics of the data manifold through the graph Laplacian constructed by the sparse codes. Experimental results on various data sets demonstrate the superiority of our algorithm compared to l1-Graph and other competing clustering methods.

[1]  David G. Stork,et al.  Pattern classification, 2nd Edition , 2000 .

[2]  Ming Liu,et al.  Regression from patch-kernel , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.

[3]  Kai Feng,et al.  SUBSPACE GAUSSIAN MIXTURE MODELS FOR SPEECH RECOGNITION , 2009 .

[4]  Zhen Li,et al.  Hierarchical Gaussianization for image classification , 2009, 2009 IEEE 12th International Conference on Computer Vision.

[5]  Shigeo Abe DrEng.  Pattern Classification , 2001, Springer London.

[6]  Yihong Gong,et al.  Linear spatial pyramid matching using sparse coding for image classification , 2009, 2009 IEEE Conference on Computer Vision and Pattern Recognition.

[7]  Adrian E. Raftery,et al.  Model-Based Clustering, Discriminant Analysis, and Density Estimation , 2002 .

[8]  Stephen P. Boyd,et al.  Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers , 2011, Found. Trends Mach. Learn..

[9]  Hujun Bao,et al.  Laplacian Regularized Gaussian Mixture Model for Data Clustering , 2011, IEEE Transactions on Knowledge and Data Engineering.

[10]  Yihong Gong,et al.  Linear spatial pyramid matching using sparse coding for image classification , 2009, CVPR.

[11]  Liang-Tien Chia,et al.  Laplacian Sparse Coding, Hypergraph Laplacian Sparse Coding, and Applications , 2013, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[12]  HeXiaofei,et al.  Laplacian Regularized Gaussian Mixture Model for Data Clustering , 2011 .

[13]  Dimitri P. Bertsekas,et al.  Nonlinear Programming , 1997 .

[14]  Mikhail Belkin,et al.  Manifold Regularization: A Geometric Framework for Learning from Labeled and Unlabeled Examples , 2006, J. Mach. Learn. Res..

[15]  Fan Chung,et al.  Spectral Graph Theory , 1996 .

[16]  Michael I. Jordan,et al.  On Spectral Clustering: Analysis and an algorithm , 2001, NIPS.

[17]  Wei-Ying Ma,et al.  Locality preserving clustering for image database , 2004, MULTIMEDIA '04.

[18]  L. Lovász.  Matching Theory (North-Holland mathematics studies) , 1986 .

[19]  Shuicheng Yan,et al.  Semi-supervised Learning by Sparse Representation , 2009, SDM.

[20]  Deng Cai,et al.  Gaussian Mixture Model with Local Consistency , 2010, AAAI.

[21]  Christopher M. Bishop,et al.  Pattern Recognition and Machine Learning (Information Science and Statistics) , 2006 .

[22]  Shuicheng Yan,et al.  Learning With $\ell ^{1}$-Graph for Image Analysis , 2010, IEEE Transactions on Image Processing.

[23]  Chun Chen,et al.  Graph Regularized Sparse Coding for Image Representation , 2011, IEEE Transactions on Image Processing.