Distance metric learning with eigenvalue optimization

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...

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Bibliographic Details
Main Authors: Yiming Ying, Peng Li, Sören Sonnenburg, Francis Bach, Cheng Soon Ong
Other Authors: The Pennsylvania State University CiteSeerX Archives
Format: Text
Language:English
Published: 2012
Subjects:
metric learning
convex optimization
semi-definite programming
first-order methods
eigenvalue optimization
DML
Online Access:http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.413.7512
http://jmlr.org/papers/volume13/ying12a/ying12a.pdf
Description
Summary: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).

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