Nested Barycentric Coordinate System as an Explicit Feature Map

Lee-Ad Gottlieb, Eran Kaufman, Aryeh Kontorovich, Gabriel Nivasch, Ofir Pele

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We introduce a new embedding technique based on barycentric coordinate system. We show that our embedding can be used to transforms the problem of polytope approximation into that of finding a linear classifier in a higher (but nevertheless quite sparse) dimensional representation. This embedding in effect maps a piecewise linear function into a single linear function, and allows us to invoke well-known algorithms for the latter problem to solve the former. We demonstrate that our embedding has applications to the problems of approximating separating polytopes – in fact, it can approximate any convex body and multiple convex bodies – as well as to classification by separating polytopes and piecewise linear regression.
Original languageEnglish GB
Title of host publicationProceedings of The 24th International Conference on Artificial Intelligence and Statistics
EditorsArindam Banerjee, Kenji Fukumizu
PublisherPMLR
Pages766-774
Number of pages9
Volume130
StatePublished - 2021

Publication series

NameProceedings of Machine Learning Research
PublisherPMLR

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