Nested Barycentric Coordinate System as an Explicit Feature mAP
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.
Cite
Text
Gottlieb et al. "Nested Barycentric Coordinate System as an Explicit Feature mAP." Artificial Intelligence and Statistics, 2021.Markdown
[Gottlieb et al. "Nested Barycentric Coordinate System as an Explicit Feature mAP." Artificial Intelligence and Statistics, 2021.](https://mlanthology.org/aistats/2021/gottlieb2021aistats-nested/)BibTeX
@inproceedings{gottlieb2021aistats-nested,
title = {{Nested Barycentric Coordinate System as an Explicit Feature mAP}},
author = {Gottlieb, Lee-Ad and Kaufman, Eran and Kontorovich, Aryeh and Nivasch, Gabriel and Pele, Ofir},
booktitle = {Artificial Intelligence and Statistics},
year = {2021},
pages = {766-774},
volume = {130},
url = {https://mlanthology.org/aistats/2021/gottlieb2021aistats-nested/}
}