Metric Embedding for Nearest Neighbor Classification

Bharath K. Sriperumbudur; Gert R. G. Lanckriet

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arXiv · 0706.3499

Metric Embedding for Nearest Neighbor Classification

Bharath K. Sriperumbudur·Gert R. G. Lanckriet

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Abstract

The distance metric plays an important role in nearest neighbor (NN) classification. Usually the Euclidean distance metric is assumed or a Mahalanobis distance metric is optimized to improve the NN performance. In this paper, we study the problem of embedding arbitrary metric spaces into a Euclidean space with the goal to improve the accuracy of the NN classifier. We propose a solution by appealing to the framework of regularization in a reproducing kernel Hilbert space and prove a representer-like theorem for NN classification. The embedding function is then determined by solving a semidefinite program which has an interesting connection to the soft-margin linear binary support vector machine classifier. Although the main focus of this paper is to present a general, theoretical framework for metric embedding in a NN setting, we demonstrate the performance of the proposed method on some benchmark datasets and show that it performs better than the Mahalanobis metric learning algorithm in terms of leave-one-out and generalization errors.

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BibTeX RIS

Bharath K. Sriperumbudur, Gert R. G. Lanckriet. 2007-06-24. Metric Embedding for Nearest Neighbor Classification. https://arxiv.org/abs/0706.3499

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