Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection
IEEE Transactions on Pattern Analysis and Machine Intelligence
From Few to Many: Illumination Cone Models for Face Recognition under Variable Lighting and Pose
IEEE Transactions on Pattern Analysis and Machine Intelligence
Lagrangian support vector machines
The Journal of Machine Learning Research
The CMU Pose, Illumination, and Expression Database
IEEE Transactions on Pattern Analysis and Machine Intelligence
Convex Optimization
Pursuing Informative Projection on Grassmann Manifold
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 2
Graph Embedding and Extensions: A General Framework for Dimensionality Reduction
IEEE Transactions on Pattern Analysis and Machine Intelligence
Linear dimensionality reduction for multi-label classification
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Optimization algorithms exploiting unitary constraints
IEEE Transactions on Signal Processing
Orthogonal Laplacianfaces for Face Recognition
IEEE Transactions on Image Processing
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Learning robust subspaces to maximize class discrimination is challenging, and most current works consider a weak connection between dimensionality reduction and classifier design. We propose an alternate framework wherein these two steps are combined in a joint formulation to exploit the direct connection between dimensionality reduction and classification. Specifically, we learn an optimal subspace on the Grassmann manifold jointly minimizing the classification error of an SVM classifier. We minimize the regularized empirical risk over both the hypothesis space of functions that underlies this new generalized multi-class Lagrangian SVM and the Grassmann manifold such that a linear projection is to be found. We propose an iterative algorithm to meet the dual goal of optimizing both the classifier and projection. Extensive numerical studies on challenging datasets show robust performance of the proposed scheme over other alternatives in contexts wherein limited training data is used, verifying the advantage of the joint formulation.