Graph embedding discriminant analysis on Grassmannian manifolds for improved image set matching

A convenient way of dealing with image sets is to represent them as points on Grassmannian manifolds. While several recent studies explored the applicability of discriminant analysis on such manifolds, the conventional formalism of discriminant analysis suffers from not considering the local structure of the data. We propose a discriminant analysis approach on Grassmannian manifolds, based on a graph-embedding framework. We show that by introducing within-class and between-class similarity graphs to characterise intra-class compactness and inter-class separability, the geometrical structure of data can be exploited. Experiments on several image datasets (PIE, BANCA, MoBo, ETH-80) show that the proposed algorithm obtains considerable improvements in discrimination accuracy, in comparison to three recent methods: Grassmann Discriminant Analysis (GDA), Kernel GDA, and the kernel version of Affine Hull Image Set Distance. We further propose a Grassmannian kernel, based on canonical correlation between subspaces, which can increase discrimination accuracy when used in combination with previous Grassmannian kernels.

[1]  Bruce A. Draper,et al.  Image-set matching using a geodesic distance and cohort normalization , 2008, 2008 8th IEEE International Conference on Automatic Face & Gesture Recognition.

[2]  Shun-ichi Amari,et al.  Methods of information geometry , 2000 .

[3]  Kun Zhou,et al.  Locality Sensitive Discriminant Analysis , 2007, IJCAI.

[4]  Bernt Schiele,et al.  Analyzing appearance and contour based methods for object categorization , 2003, 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings..

[5]  Shimon Ullman,et al.  Face Recognition: The Problem of Compensating for Changes in Illumination Direction , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

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

[7]  Nello Cristianini,et al.  Kernel Methods for Pattern Analysis , 2003, ICTAI.

[8]  Ken-ichi Maeda,et al.  Face recognition using temporal image sequence , 1998, Proceedings Third IEEE International Conference on Automatic Face and Gesture Recognition.

[9]  Jieping Ye,et al.  Integrating Global and Local Structures: A Least Squares Framework for Dimensionality Reduction , 2007, 2007 IEEE Conference on Computer Vision and Pattern Recognition.

[10]  Daniel D. Lee,et al.  Extended Grassmann Kernels for Subspace-Based Learning , 2008, NIPS.

[11]  Brian C. Lovell,et al.  Multi-Region Probabilistic Histograms for Robust and Scalable Identity Inference , 2009, ICB.

[12]  Lior Wolf,et al.  Learning over Sets using Kernel Principal Angles , 2003, J. Mach. Learn. Res..

[13]  Hakan Cevikalp,et al.  Face recognition based on image sets , 2010, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[14]  Pengfei Shi,et al.  Kernel Grassmannian distances and discriminant analysis for face recognition from image sets , 2009, Pattern Recognit. Lett..

[15]  Samy Bengio,et al.  User authentication via adapted statistical models of face images , 2006, IEEE Transactions on Signal Processing.

[16]  Michael I. Jordan,et al.  Distance Metric Learning with Application to Clustering with Side-Information , 2002, NIPS.

[17]  Jiri Matas,et al.  On Combining Classifiers , 1998, IEEE Trans. Pattern Anal. Mach. Intell..

[18]  Ana Bernardis,et al.  Perturbations of the Haar wavelet by convolution , 2001 .

[19]  Jean-Philippe Thiran,et al.  The BANCA Database and Evaluation Protocol , 2003, AVBPA.

[20]  Radford M. Neal Pattern Recognition and Machine Learning , 2007, Technometrics.

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

[22]  Stephen Lin,et al.  Graph Embedding and Extensions: A General Framework for Dimensionality Reduction , 2007, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[23]  Terence Sim,et al.  The CMU Pose, Illumination, and Expression Database , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[24]  Daniel D. Lee,et al.  Grassmann discriminant analysis: a unifying view on subspace-based learning , 2008, ICML '08.

[25]  Wen Gao,et al.  Manifold-Manifold Distance with application to face recognition based on image set , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.

[26]  Josef Kittler,et al.  Discriminative Learning and Recognition of Image Set Classes Using Canonical Correlations , 2007, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[27]  S. Rosenberg The Laplacian on a Riemannian Manifold: An Introduction to Analysis on Manifolds , 1997 .

[28]  Trevor Darrell,et al.  Face recognition with image sets using manifold density divergence , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[29]  Masashi Sugiyama,et al.  Dimensionality Reduction of Multimodal Labeled Data by Local Fisher Discriminant Analysis , 2007, J. Mach. Learn. Res..

[30]  Ralph Gross,et al.  The CMU Motion of Body (MoBo) Database , 2001 .

[31]  Majid Nili Ahmadabadi,et al.  Optimal Local Basis: A Reinforcement Learning Approach for Face Recognition , 2009, International Journal of Computer Vision.