Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection
IEEE Transactions on Pattern Analysis and Machine Intelligence
The Geometry of Algorithms with Orthogonality Constraints
SIAM Journal on Matrix Analysis and Applications
Kernel Eigenfaces vs. Kernel Fisherfaces: Face Recognition Using Kernel Methods
FGR '02 Proceedings of the Fifth IEEE International Conference on Automatic Face and Gesture Recognition
The CMU Pose, Illumination, and Expression (PIE) Database
FGR '02 Proceedings of the Fifth IEEE International Conference on Automatic Face and Gesture Recognition
A Unified Framework for Subspace Face Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Face Recognition Using Laplacianfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Graph Embedding: A General Framework for Dimensionality Reduction
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
An optimization criterion for generalized discriminant analysis on undersampled problems
IEEE Transactions on Pattern Analysis and Machine Intelligence
Face recognition using kernel direct discriminant analysis algorithms
IEEE Transactions on Neural Networks
Efficient and robust feature extraction by maximum margin criterion
IEEE Transactions on Neural Networks
Supervised dimensionality reduction via sequential semidefinite programming
Pattern Recognition
Learning a Mahalanobis distance metric for data clustering and classification
Pattern Recognition
Semi-supervised orthogonal discriminant analysis via label propagation
Pattern Recognition
A novel kernel-based maximum a posteriori classification method
Neural Networks
Canonical Stiefel quotient and its application to generic face recognition in illumination spaces
BTAS'09 Proceedings of the 3rd IEEE international conference on Biometrics: Theory, applications and systems
A convex programming approach to the trace quotient problem
ACCV'07 Proceedings of the 8th Asian conference on Computer vision - Volume Part II
A novel local sensitive frontier analysis for feature extraction
ICIC'09 Proceedings of the Intelligent computing 5th international conference on Emerging intelligent computing technology and applications
The Trace Ratio Optimization Problem for Dimensionality Reduction
SIAM Journal on Matrix Analysis and Applications
A variant of the trace quotient formulation for dimensionality reduction
ACCV'09 Proceedings of the 9th Asian conference on Computer Vision - Volume Part III
Advances in matrix manifolds for computer vision
Image and Vision Computing
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The formulation of trace quotient is shared by many computer vision problems; however, it was conventionally approximated by an essentially different formulation of quotient trace, which can be solved with the generalized eigenvalue decomposition approach. In this paper, we present a direct solution to the former formulation. First, considering that the feasible solutions are constrained on a Grassmann manifold, we present a necessary condition for the optimal solution of the trace quotient problem, which then naturally elicits an iterative procedure for pursuing the optimal solution. The proposed algorithm, referred to as Optimal Projection Pursuing (OPP), has the following characteristics: 1) OPP directly optimizes the trace quotient, and is theoretically optimal; 2) OPP does not suffer from the solution uncertainty issue existing in the quotient trace formulation that the objective function value is invariant under any nonsingular linear transformation, and OPP is invariant only under orthogonal transformations, which does not affect final distance measurement; and 3) OPP reveals the underlying equivalence between the trace quotient problem and the corresponding trace difference problem. Extensive experiments on face recognition validate the superiority of OPP over the solution of the corresponding quotient trace problem in both objective function value and classification capability.