Graph Regularized Subspace Clustering via Low-Rank Decomposition

Subspace clustering (SC) is able to identify low-dimensional subspace structures embedded in high-dimensional data. Recently, graph-regularized approaches aim to tackle this problem by learning a linear representation of data samples and also a graph structure in a unified framework. However, previous approaches exploit a graph embedding term based on representation matrix, which could over-smooth the graph structure and thus adversely affect the clustering performance. In this paper, we present a novel algorithm based on joint low-rank decomposition and graph learning from data samples. In graph learning, only a low-rank component of the representation matrix is employed to construct the graph embedding term. An alternating direction method of multipliers (ADMM) is further developed to tackle the resulting nonconvex problem. Experimental results on both synthetic data and real benchmark databases validate the effectiveness of the proposed SC algorithm.

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

[2]  Takeo Kanade,et al.  A Multibody Factorization Method for Independently Moving Objects , 1998, International Journal of Computer Vision.

[3]  Pascal Frossard,et al.  Learning Graphs From Data: A Signal Representation Perspective , 2018, IEEE Signal Processing Magazine.

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

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

[6]  A. Martínez,et al.  The AR face databasae , 1998 .

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

[8]  David J. Kriegman,et al.  Acquiring linear subspaces for face recognition under variable lighting , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[9]  Jun Wang,et al.  LRSR: Low-Rank-Sparse representation for subspace clustering , 2016, Neurocomputing.

[10]  Junbin Gao,et al.  Subspace Clustering via Learning an Adaptive Low-Rank Graph , 2018, IEEE Transactions on Image Processing.

[11]  Xiaojie Guo,et al.  Robust Subspace Segmentation by Simultaneously Learning Data Representations and Their Affinity Matrix , 2015, IJCAI.

[12]  Georgios B. Giannakis,et al.  Topology Identification and Learning over Graphs: Accounting for Nonlinearities and Dynamics , 2018, Proceedings of the IEEE.

[13]  Aleix M. Martinez,et al.  The AR face database , 1998 .

[14]  René Vidal,et al.  Combined central and subspace clustering for computer vision applications , 2006, ICML.

[15]  Feiping Nie,et al.  The Constrained Laplacian Rank Algorithm for Graph-Based Clustering , 2016, AAAI.

[16]  Sameer A. Nene,et al.  Columbia Object Image Library (COIL100) , 1996 .

[17]  Huan Liu,et al.  Subspace clustering for high dimensional data: a review , 2004, SKDD.

[18]  Shuicheng Yan,et al.  Robust and Efficient Subspace Segmentation via Least Squares Regression , 2012, ECCV.

[19]  Zongze Wu,et al.  Sparse subspace clustering with jointly learning representation and affinity matrix , 2018, J. Frankl. Inst..

[20]  René Vidal,et al.  Motion segmentation via robust subspace separation in the presence of outlying, incomplete, or corrupted trajectories , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.

[21]  Feiping Nie,et al.  Clustering and projected clustering with adaptive neighbors , 2014, KDD.

[22]  Jonathan J. Hull,et al.  A Database for Handwritten Text Recognition Research , 1994, IEEE Trans. Pattern Anal. Mach. Intell..