Nested Barycentric Coordinate System as an Explicit Feature Map

Research output: Contribution to journalConference articlepeer-review


We introduce a new embedding technique based on a barycentric coordinate system. We show that our embedding can be used to transform the problem of polytope approximation into one of finding a linear classifier in a higher dimensional (but nevertheless quite sparse) representation. In effect, this embedding maps a piecewise linear function into an everywhere-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 unions of convex bodies - as well as to classification by separating polytopes and piecewise linear regression.

Original languageEnglish
Pages (from-to)766-774
Number of pages9
JournalProceedings of Machine Learning Research
StatePublished - 1 Jan 2021
Event24th International Conference on Artificial Intelligence and Statistics, AISTATS 2021 - Virtual, Online, United States
Duration: 13 Apr 202115 Apr 2021

All Science Journal Classification (ASJC) codes

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability


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