Semi-supervised Sparse Subspace Clustering on Symmetric Positive Definite Manifolds

The covariance descriptor which is a symmetric positive definite (SPD) matrix, has recently attracted considerable attentions in computer vision. However, it is not trivial issue to handle its non-linearity in semi-supervised learning. To this end, in this paper, a semi-supervised sparse subspace clustering on SPD manifolds is proposed, via considering the intrinsic geometric structure within the manifold-valued data. Experimental results on two databases show that our method can provide better clustering solutions than the state-of-the-art approaches thanks to incorporating Riemannian geometry structure.

[1]  Jitendra Malik,et al.  Normalized Cuts and Image Segmentation , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[2]  René Vidal,et al.  Kernel sparse subspace clustering , 2014, 2014 IEEE International Conference on Image Processing (ICIP).

[3]  Michael Elad,et al.  Stable recovery of sparse overcomplete representations in the presence of noise , 2006, IEEE Transactions on Information Theory.

[4]  René Vidal,et al.  Low rank subspace clustering (LRSC) , 2014, Pattern Recognit. Lett..

[5]  Yong Yu,et al.  Robust Recovery of Subspace Structures by Low-Rank Representation , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[6]  Xiaojin Zhu,et al.  --1 CONTENTS , 2006 .

[7]  Yong Yu,et al.  Robust Subspace Segmentation by Low-Rank Representation , 2010, ICML.

[8]  Rong Jin,et al.  Semi-Supervised Clustering , 2015 .

[9]  Bo Li,et al.  Information Theoretic Subspace Clustering , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[10]  Anoop Cherian,et al.  Riemannian Sparse Coding for Positive Definite Matrices , 2014, ECCV.

[11]  Zoubin Ghahramani,et al.  Combining active learning and semi-supervised learning using Gaussian fields and harmonic functions , 2003, ICML 2003.

[12]  Baba C. Vemuri,et al.  On A Nonlinear Generalization of Sparse Coding and Dictionary Learning , 2013, ICML.

[13]  Lei Zhang,et al.  Log-Euclidean Kernels for Sparse Representation and Dictionary Learning , 2013, 2013 IEEE International Conference on Computer Vision.

[14]  Junbin Gao,et al.  Nonlinear low-rank representation on Stiefel manifolds , 2015 .

[15]  René Vidal,et al.  Subspace Clustering , 2011, IEEE Signal Processing Magazine.

[16]  Brian C. Lovell,et al.  Sparse Coding and Dictionary Learning for Symmetric Positive Definite Matrices: A Kernel Approach , 2012, ECCV.

[17]  X. Hong,et al.  Low Rank Representation on Riemannian Manifold of Symmetric Positive Definite Matrices , 2015, SDM 2015.

[18]  Fatih Murat Porikli,et al.  Pedestrian Detection via Classification on Riemannian Manifolds , 2008, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[19]  Vassilios Morellas,et al.  Tensor Sparse Coding for Positive Definite Matrices , 2014, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[20]  Junbin Gao,et al.  Kernel Sparse Subspace Clustering on Symmetric Positive Definite Manifolds , 2016, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[21]  René Vidal,et al.  Sparse Subspace Clustering: Algorithm, Theory, and Applications , 2012, IEEE transactions on pattern analysis and machine intelligence.

[22]  Hongdong Li,et al.  Kernel Methods on the Riemannian Manifold of Symmetric Positive Definite Matrices , 2013, 2013 IEEE Conference on Computer Vision and Pattern Recognition.

[23]  Fei Wang,et al.  Learning Spectral Embedding for Semi-supervised Clustering , 2011, 2011 IEEE 11th International Conference on Data Mining.

[24]  M. R. Osborne,et al.  A new approach to variable selection in least squares problems , 2000 .

[25]  Changyin Sun,et al.  Kernel Low-Rank Representation for face recognition , 2015, Neurocomputing.

[26]  Simon C. K. Shiu,et al.  Gabor feature based robust representation and classification for face recognition with Gabor occlusion dictionary , 2013, Pattern Recognit..

[27]  Nicholas Ayache,et al.  Geometric Means in a Novel Vector Space Structure on Symmetric Positive-Definite Matrices , 2007, SIAM J. Matrix Anal. Appl..

[28]  Xavier Pennec,et al.  A Riemannian Framework for Tensor Computing , 2005, International Journal of Computer Vision.

[29]  Suvrit Sra,et al.  A new metric on the manifold of kernel matrices with application to matrix geometric means , 2012, NIPS.

[30]  Junbin Gao,et al.  Dual Graph Regularized Latent Low-Rank Representation for Subspace Clustering , 2015, IEEE Transactions on Image Processing.

[31]  Brian C. Lovell,et al.  Sparse Coding on Symmetric Positive Definite Manifolds Using Bregman Divergences , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[32]  Anoop Cherian,et al.  Jensen-Bregman LogDet Divergence with Application to Efficient Similarity Search for Covariance Matrices , 2013, IEEE Transactions on Pattern Analysis and Machine Intelligence.