Transformation invariant subspace clustering

Subspace clustering has achieved great success in many computer vision applications. However, most subspace clustering algorithms require well aligned data samples, which is often not straightforward to achieve. This paper proposes a Transformation Invariant Subspace Clustering framework by jointly aligning data samples and learning subspace representation. By alignment, the transformed data samples become highly correlated and a better affinity matrix can be obtained. The joint problem can be reduced to a sequence of Least Squares Regression problems, which can be efficiently solved. We verify the effectiveness of the proposed method with extensive experiments on unaligned real data, demonstrating its higher clustering accuracy than the state-of-the-art subspace clustering and transformation invariant clustering algorithms. HighlightsA transformation invariant subspace clustering algorithm is proposed.Alignment and subspace clustering are mutually dependent.State-of-the-art clustering results on the unconstrained face dataset.

[1]  Zhenan Sun,et al.  Robust Subspace Clustering With Complex Noise , 2015, IEEE Transactions on Image Processing.

[2]  David Zhang,et al.  Efficient Misalignment-Robust Representation for Real-Time Face Recognition , 2012, ECCV.

[3]  S. Shankar Sastry,et al.  Generalized principal component analysis (GPCA) , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

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

[5]  Shuicheng Yan,et al.  Correlation Adaptive Subspace Segmentation by Trace Lasso , 2013, 2013 IEEE International Conference on Computer Vision.

[6]  Hossein Mobahi,et al.  Toward a Practical Face Recognition System: Robust Alignment and Illumination by Sparse Representation , 2012, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[7]  Shiguang Shan,et al.  Coupling Alignments with Recognition for Still-to-Video Face Recognition , 2013, 2013 IEEE International Conference on Computer Vision.

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

[9]  Paul A. Viola,et al.  Robust Real-Time Face Detection , 2001, Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001.

[10]  Rudolf Mester,et al.  Discriminative Subspace Clustering , 2013, 2013 IEEE Conference on Computer Vision and Pattern Recognition.

[11]  Yongtian Wang,et al.  Layered Graph Match with Graph Editing , 2007, 2007 IEEE Conference on Computer Vision and Pattern Recognition.

[12]  David J. Kriegman,et al.  Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection , 1996, ECCV.

[13]  J KriegmanDavid,et al.  Eigenfaces vs. Fisherfaces , 1997 .

[14]  Junzhou Huang,et al.  Simultaneous image transformation and sparse representation recovery , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.

[15]  Liang Lin,et al.  Human Re-identification by Matching Compositional Template with Cluster Sampling , 2013, 2013 IEEE International Conference on Computer Vision.

[16]  Liang Lin,et al.  Layered Graph Matching with Composite Cluster Sampling , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[17]  Sridha Sridharan,et al.  Least squares congealing for unsupervised alignment of images , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.

[18]  Zhang Yi,et al.  Robust Subspace Clustering via Thresholding Ridge Regression , 2015, AAAI.

[19]  Marc Pollefeys,et al.  A General Framework for Motion Segmentation: Independent, Articulated, Rigid, Non-rigid, Degenerate and Non-degenerate , 2006, ECCV.

[20]  Marwan Mattar,et al.  Labeled Faces in the Wild: A Database forStudying Face Recognition in Unconstrained Environments , 2008 .

[21]  LuJiwen,et al.  Transform-Invariant PCA , 2014 .

[22]  Jianjiang Feng,et al.  Smooth Representation Clustering , 2014, 2014 IEEE Conference on Computer Vision and Pattern Recognition.

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

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

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

[26]  Allen R. Hanson,et al.  Unsupervised Joint Alignment and Clustering using Bayesian Nonparametrics , 2012, UAI.

[27]  Kenichi Kanatani,et al.  Geometric Structure of Degeneracy for Multi-body Motion Segmentation , 2004, ECCV Workshop SMVP.

[28]  Jian-Huang Lai,et al.  Face hallucination with imprecise-alignment using iterative sparse representation , 2014, Pattern Recognit..

[29]  Tieniu Tan,et al.  Half-Quadratic-Based Iterative Minimization for Robust Sparse Representation , 2014, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[30]  Tieniu Tan,et al.  Robust Recovery of Corrupted Low-RankMatrix by Implicit Regularizers , 2014, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[31]  Takeo Kanade,et al.  Multi-PIE , 2008, 2008 8th IEEE International Conference on Automatic Face & Gesture Recognition.

[32]  David J. Kriegman,et al.  Recognition using class specific linear projection , 1997 .

[33]  Ognjen Arandjelovic,et al.  Multiple-object Tracking in Cluttered and Crowded Public Spaces , 2010, ISVC.

[34]  Yi Ma,et al.  TILT: Transform Invariant Low-Rank Textures , 2010, ACCV.

[35]  Takeo Kanade,et al.  An Iterative Image Registration Technique with an Application to Stereo Vision , 1981, IJCAI.

[36]  R. Vidal,et al.  Sparse Subspace Clustering: Algorithm, Theory, and Applications. , 2013, IEEE transactions on pattern analysis and machine intelligence.

[37]  Tieniu Tan,et al.  Joint Alignment and Clustering via Low-Rank Representation , 2013, 2013 2nd IAPR Asian Conference on Pattern Recognition.

[38]  Allen Y. Yang,et al.  Estimation of Subspace Arrangements with Applications in Modeling and Segmenting Mixed Data , 2008, SIAM Rev..

[39]  Simon Baker,et al.  Lucas-Kanade 20 Years On: A Unifying Framework , 2004, International Journal of Computer Vision.

[40]  John Wright,et al.  RASL: Robust Alignment by Sparse and Low-Rank Decomposition for Linearly Correlated Images , 2012, IEEE Trans. Pattern Anal. Mach. Intell..

[41]  Liang Lin,et al.  Layered graph matching by composite cluster sampling with collaborative and competitive interactions , 2009, 2009 IEEE Conference on Computer Vision and Pattern Recognition.

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

[43]  Allen Y. Yang,et al.  Robust Face Recognition via Sparse Representation , 2009, IEEE Transactions on Pattern Analysis and Machine Intelligence.

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

[45]  René Vidal,et al.  Structured Sparse Subspace Clustering: A unified optimization framework , 2015, 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[46]  David J. Kriegman,et al.  Clustering appearances of objects under varying illumination conditions , 2003, 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings..

[47]  Shuicheng Yan,et al.  Robust Subspace Segmentation with Block-Diagonal Prior , 2014, 2014 IEEE Conference on Computer Vision and Pattern Recognition.

[48]  Bin Shen,et al.  Online robust image alignment via iterative convex optimization , 2012, 2012 IEEE Conference on Computer Vision and Pattern Recognition.

[49]  B. Frey,et al.  Transformation-Invariant Clustering Using the EM Algorithm , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[50]  Jiwen Lu,et al.  Transform-Invariant PCA: A Unified Approach to Fully Automatic FaceAlignment, Representation, and Recognition , 2014, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[51]  Shree K. Nayar,et al.  Attribute and simile classifiers for face verification , 2009, 2009 IEEE 12th International Conference on Computer Vision.

[52]  Roberto Cipolla,et al.  Achieving robust face recognition from video by combining a weak photometric model and a learnt generic face invariant , 2013, Pattern Recognit..

[53]  Shuicheng Yan,et al.  SOLD: Sub-optimal low-rank decomposition for efficient video segmentation , 2015, 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[54]  Roberto Tron RenVidal.  A Benchmark for the Comparison of 3-D Motion Segmentation Algorithms , 2007 .

[55]  Tieniu Tan,et al.  Robust Subspace Clustering via Half-Quadratic Minimization , 2013, 2013 IEEE International Conference on Computer Vision.

[56]  Christopher M. Bishop,et al.  Mixtures of Probabilistic Principal Component Analyzers , 1999, Neural Computation.

[57]  Constantine Caramanis,et al.  Greedy Subspace Clustering , 2014, NIPS.

[58]  Yoshua Bengio,et al.  Gradient-based learning applied to document recognition , 1998, Proc. IEEE.

[59]  MatthewsIain,et al.  Lucas-Kanade 20 Years On , 2004 .

[60]  Y. Weiss,et al.  Multibody factorization with uncertainty and missing data using the EM algorithm , 2004, CVPR 2004.

[61]  Xiaoming Liu,et al.  Simultaneous alignment and clustering for an image ensemble , 2009, 2009 IEEE 12th International Conference on Computer Vision.

[62]  Tieniu Tan,et al.  Robust Recovery of Corrupted Low-rank Matrix by Implicit Regularizers. , 2013, IEEE transactions on pattern analysis and machine intelligence.

[63]  Erik G. Learned-Miller,et al.  Data driven image models through continuous joint alignment , 2006, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[64]  Shuicheng Yan,et al.  Correntropy Induced L2 Graph for Robust Subspace Clustering , 2013, 2013 IEEE International Conference on Computer Vision.

[65]  René Vidal,et al.  Sparse subspace clustering , 2009, CVPR.

[66]  Jian-Huang Lai,et al.  Learning contour-fragment-based shape model with And-Or tree representation , 2012, 2012 IEEE Conference on Computer Vision and Pattern Recognition.

[67]  Stefano Soatto,et al.  Joint data alignment up to (lossy) transformations , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.