Adaptive metric dimensionality reduction

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Adaptive metric dimensionality reduction
Abstract. We study data-adaptive 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, which yields a new theoretical explanation for empirically reported improvements gained by preprocessing Euclidean data by PCA (Principal Components Analysis) prior to constructing a linear classifier. 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.
Lee-Ad Gottlieb, Aryeh Kontorovich, Robert Krauthg
Added 10 Apr 2016
Updated 10 Apr 2016
Type Journal
Year 2016
Where TCS
Authors Lee-Ad Gottlieb, Aryeh Kontorovich, Robert Krauthgamer
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