Topics in matrix analysis
On minimizing the maximum eigenvalue of a symmetric matrix
SIAM Journal on Matrix Analysis and Applications
A Spectral Bundle Method for Semidefinite Programming
SIAM Journal on Optimization
Multiresolution Gray-Scale and Rotation Invariant Texture Classification with Local Binary Patterns
IEEE Transactions on Pattern Analysis and Machine Intelligence
Learning a kernel matrix for nonlinear dimensionality reduction
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Online and batch learning of pseudo-metrics
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Smooth minimization of non-smooth functions
Mathematical Programming: Series A and B
Learning a Similarity Metric Discriminatively, with Application to Face Verification
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
Learning a Mahalanobis Metric from Equivalence Constraints
The Journal of Machine Learning Research
Learning sparse metrics via linear programming
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
Learning Distance Metrics with Contextual Constraints for Image Retrieval
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 2
Smoothing Technique and its Applications in Semidefinite Optimization
Mathematical Programming: Series A and B
Information-theoretic metric learning
Proceedings of the 24th international conference on Machine learning
Fast solvers and efficient implementations for distance metric learning
Proceedings of the 25th international conference on Machine learning
Consistency of Trace Norm Minimization
The Journal of Machine Learning Research
IEEE Transactions on Pattern Analysis and Machine Intelligence
Sparse approximate solutions to semidefinite programs
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Metric learning for enzyme active-site search
Bioinformatics
Similarity scores based on background samples
ACCV'09 Proceedings of the 9th Asian conference on Computer Vision - Volume Part II
Online Regularized Classification Algorithms
IEEE Transactions on Information Theory
Supervised earth mover's distance learning and its computer vision applications
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part I
Bayesian face revisited: a joint formulation
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part III
Distance metric learning revisited
ECML PKDD'12 Proceedings of the 2012 European conference on Machine Learning and Knowledge Discovery in Databases - Volume Part I
Max-margin embedding for multi-label learning
Pattern Recognition Letters
Geometry preserving multi-task metric learning
Machine Learning
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The main theme of this paper is to develop a novel eigenvalue optimization framework for learning a Mahalanobis metric. Within this context, we introduce a novel metric learning approach called DML-eig which is shown to be equivalent to a well-known eigenvalue optimization problem called minimizing the maximal eigenvalue of a symmetric matrix (Overton, 1988; Lewis and Overton, 1996). Moreover, we formulate LMNN (Weinberger et al., 2005), one of the state-of-the-art metric learning methods, as a similar eigenvalue optimization problem. This novel framework not only provides new insights into metric learning but also opens new avenues to the design of efficient metric learning algorithms. Indeed, first-order algorithms are developed for DML-eig and LMNN which only need the computation of the largest eigenvector of a matrix per iteration. Their convergence characteristics are rigorously established. Various experiments on benchmark data sets show the competitive performance of our new approaches. In addition, we report an encouraging result on a difficult and challenging face verification data set called Labeled Faces in the Wild (LFW).