Efficient classification for metric data

Lee Ad Gottlieb, Aryeh Kontorovich, Robert Krauthgamer

Research output: Contribution to journalArticlepeer-review

35 Scopus citations

Abstract

Recent advances in large-margin classification of data residing in general metric spaces (rather than Hilbert spaces) enable classification under various natural metrics, such as string edit and earthmover distance. A general framework developed for this purpose left open the questions of computational efficiency and of providing direct bounds on generalization error. We design a new algorithm for classification in general metric spaces, whose runtime and accuracy depend on the doubling dimension of the data points, and can thus achieve superior classification performance in many common scenarios. The algorithmic core of our approach is an approximate (rather than exact) solution to the classical problems of Lipschitz extension and of nearest neighbor search. The algorithm's generalization performance is guaranteed via the fat-shattering dimension of Lipschitz classifiers, and we present experimental evidence of its superiority to some common kernel methods. As a by-product, we offer a new perspective on the nearest neighbor classifier, which yields significantly sharper risk asymptotics than the classic analysis.

Original languageEnglish
Article number6867374
Pages (from-to)5750-5759
Number of pages10
JournalIEEE Transactions on Information Theory
Volume60
Issue number9
DOIs
StatePublished - 1 Jan 2014

Keywords

  • Classification
  • Lipschitz function
  • doubling dimension
  • metric space

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