On the sum of the largest eigenvalues of a symmetric matrix
SIAM Journal on Matrix Analysis and Applications
Mathematical Programming: Series A and B - Special issue: Festschrift in Honor of Philip Wolfe part II: studies in nonlinear programming
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
SVM-based Nonparametric Discriminant Analysis, An Application to Face Detection
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Binary Partitioning, Perceptual Grouping, and Restoration with Semidefinite Programming
IEEE Transactions on Pattern Analysis and Machine Intelligence
Convex Optimization
Learning the Kernel Matrix with Semidefinite Programming
The Journal of Machine Learning Research
Margin based feature selection - theory and algorithms
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Non-negative Matrix Factorization with Sparseness Constraints
The Journal of Machine Learning Research
Learning Non-Negative Sparse Image Codes by Convex Programming
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
Unsupervised Learning of Image Manifolds by Semidefinite Programming
International Journal of Computer Vision
Null space versus orthogonal linear discriminant analysis
ICML '06 Proceedings of the 23rd international conference on Machine learning
Graph Embedding and Extensions: A General Framework for Dimensionality Reduction
IEEE Transactions on Pattern Analysis and Machine Intelligence
Controlling sparseness in non-negative tensor factorization
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
Practical global optimization for multiview geometry
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
Trace quotient problems revisited
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part II
Orthogonal Laplacianfaces for Face Recognition
IEEE Transactions on Image Processing
Efficient and robust feature extraction by maximum margin criterion
IEEE Transactions on Neural Networks
Semi-supervised orthogonal discriminant analysis via label propagation
Pattern Recognition
Feature selection with redundancy-constrained class separability
IEEE Transactions on Neural Networks
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
Feature selection with SVD entropy: Some modification and extension
Information Sciences: an International Journal
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Many dimensionality reduction problems end up with a trace quotient formulation. Since it is difficult to directly solve the trace quotient problem, traditionally the trace quotient cost function is replaced by an approximation such that the generalized eigenvalue decomposition can be applied. In contrast, we directly optimize the trace quotient in this work. It is reformulated as a quasi-linear semidefinite optimization problem, which can be solved globally and efficiently using standard off-the-shelf semidefinite programming solvers. Also this optimization strategy allows one to enforce additional constraints (for example, sparseness constraints) on the projection matrix. We apply this optimization framework to a novel dimensionality reduction algorithm. The performance of the proposed algorithm is demonstrated in experiments by several UCI machine learning benchmark examples, USPS handwritten digits as well as ORL and Yale face data.