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arXiv · 1302.2752

Adaptive Metric Dimensionality Reduction

Lee-Ad Gottlieb·Aryeh Kontorovich·Robert Krauthgamer
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Abstract

We study adaptive data-dependent dimensionality reduction in the context of supervised learning in general metric spaces. Our main statistical contribution is a generalization bound for Lipschitz functions in metric spaces that are doubling, or nearly doubling. On the algorithmic front, we describe an analogue of PCA for metric spaces: namely an efficient procedure that approximates the data's intrinsic dimension, which is often much lower than the ambient dimension. Our approach thus leverages the dual benefits of low dimensionality: (1) more efficient algorithms, e.g., for proximity search, and (2) more optimistic generalization bounds.

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Lee-Ad Gottlieb, Aryeh Kontorovich, Robert Krauthgamer. 2015-03-25. Adaptive Metric Dimensionality Reduction. https://arxiv.org/abs/1302.2752

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