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Jason V. Davis

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2 papers

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JMLR Journal 2012 Journal Article

Metric and Kernel Learning Using a Linear Transformation

Prateek Jain
Brian Kulis
Jason V. Davis
Inderjit S. Dhillon

Metric and kernel learning arise in several machine learning applications. However, most existing metric learning algorithms are limited to learning metrics over low-dimensional data, while existing kernel learning algorithms are often limited to the transductive setting and do not generalize to new data points. In this paper, we study the connections between metric learning and kernel learning that arise when studying metric learning as a linear transformation learning problem. In particular, we propose a general optimization framework for learning metrics via linear transformations, and analyze in detail a special case of our framework---that of minimizing the LogDet divergence subject to linear constraints. We then propose a general regularized framework for learning a kernel matrix, and show it to be equivalent to our metric learning framework. Our theoretical connections between metric and kernel learning have two main consequences: 1) the learned kernel matrix parameterizes a linear transformation kernel function and can be applied inductively to new data points, 2) our result yields a constructive method for kernelizing most existing Mahalanobis metric learning formulations. We demonstrate our learning approach by applying it to large-scale real world problems in computer vision, text mining and semi-supervised kernel dimensionality reduction. [abs] [ pdf ][ bib ] &copy JMLR 2012. ( edit, beta )

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ICML Conference 2007 Conference Paper

Information-theoretic metric learning

Jason V. Davis
Brian Kulis
Prateek Jain 0002
Suvrit Sra
Inderjit S. Dhillon

In this paper, we present an information-theoretic approach to learning a Mahalanobis distance function. We formulate the problem as that of minimizing the differential relative entropy between two multivariate Gaussians under constraints on the distance function. We express this problem as a particular Bregman optimization problem---that of minimizing the LogDet divergence subject to linear constraints. Our resulting algorithm has several advantages over existing methods. First, our method can handle a wide variety of constraints and can optionally incorporate a prior on the distance function. Second, it is fast and scalable. Unlike most existing methods, no eigenvalue computations or semi-definite programming are required. We also present an online version and derive regret bounds for the resulting algorithm. Finally, we evaluate our method on a recent error reporting system for software called Clarify, in the context of metric learning for nearest neighbor classification, as well as on standard data sets.

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