Discriminant Additive Tangent Spaces for Object Recognition

Pattern variation is a major factor that affects the performance of recognition systems. In this paper, a novel manifold tangent modeling method called discriminant additive tangent spaces (DATS) is proposed for invariant pattern recognition. In DATS, intra-class variations for traditional tangent learning are called positive tangent samples. In addition, extra-class variations are introduced as negative tangent samples. We use log-odds to measure the significance of samples being positive or negative, and then directly characterizes this log-odds using generalized additive models (GAM). This model is estimated to maximally discriminate positive and negative samples. Besides, since traditional GAM fitting algorithm can not handle the high dimensional data in visual recognition tasks, we also present an efficient, sparse solution for GAM estimation. The resulting DATS is a nonparametric discriminant model based on quite weak prior hypotheses, hence it can depict various pattern variations effectively. Experiments demonstrate the effectiveness of our method in several recognition tasks.

[1]  D. Ruppert.  The Elements of Statistical Learning: Data Mining, Inference, and Prediction , 2004 .

[2]  Paul Dierckx,et al.  Curve and surface fitting with splines , 1994, Monographs on numerical analysis.

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

[4]  Yoshua Bengio,et al.  Non-Local Manifold Tangent Learning , 2004, NIPS.

[5]  Yann LeCun,et al.  Efficient Pattern Recognition Using a New Transformation Distance , 1992, NIPS.

[6]  Changshui Zhang,et al.  Probabilistic tangent subspace: a unified view , 2004, ICML.

[7]  P. McCullagh,et al.  Generalized Linear Models , 1984 .

[8]  Michael E. Tipping,et al.  Probabilistic Principal Component Analysis , 1999 .

[9]  Mikhail Belkin,et al.  Laplacian Eigenmaps for Dimensionality Reduction and Data Representation , 2003, Neural Computation.

[10]  Baback Moghaddam,et al.  Principal Manifolds and Probabilistic Subspaces for Visual Recognition , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[11]  Hwann-Tzong Chen,et al.  Local discriminant embedding and its variants , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

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

[13]  G. Tutz,et al.  Generalized Additive Modeling with Implicit Variable Selection by Likelihood‐Based Boosting , 2006, Biometrics.

[14]  Robert Tibshirani,et al.  The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd Edition , 2001, Springer Series in Statistics.

[15]  S T Roweis,et al.  Nonlinear dimensionality reduction by locally linear embedding. , 2000, Science.

[16]  Changshui Zhang,et al.  Visual object recognition using probabilistic kernel subspace similarity , 2005, Pattern Recognit..

[17]  David M. Young,et al.  Applied Iterative Methods , 2004 .

[18]  Alex Pentland,et al.  Probabilistic Visual Learning for Object Representation , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[19]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

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

[21]  Paul H. C. Eilers,et al.  Direct generalized additive modeling with penalized likelihood , 1998 .

[22]  Dragoslav D. Šiljak,et al.  An improved block-parallel Newton method via epsilon decompositions for load-flow calculations , 1996 .

[23]  Patrice Y. Simard,et al.  Learning Prototype Models for Tangent Distance , 1994, NIPS.

[24]  Samy Bengio,et al.  Tangent vector kernels for invariant image classification with SVMs , 2004, Proceedings of the 17th International Conference on Pattern Recognition, 2004. ICPR 2004..

[25]  D. Siljak,et al.  A Block-Parallel Newton Method via Overlapping Epsilon Decompositions , 1992, 1992 American Control Conference.

[26]  J. Tenenbaum,et al.  A global geometric framework for nonlinear dimensionality reduction. , 2000, Science.

[27]  D. Siljak,et al.  A Block-Parallel Newton Method Via OverlappingEpsilon Decompositions , 1994 .

[28]  R. Tibshirani,et al.  Generalized Additive Models , 1991 .