Nested Barycentric Coordinate System as an Explicit Feature mAP for Polyhedra Approximation and Learning Tasks
Abstract
We introduce a new embedding technique based on a nested barycentric coordinate system. We show that our embedding can be used to transform the problems of polyhedron approximation, piecewise linear classification and convex regression into one of finding a linear classifier or regressor in a higher dimensional (but nevertheless quite sparse) representation. Our 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 explain the applications of our embedding to the problems of approximating separating polyhedra—in fact, it can approximate any convex body and unions of convex bodies—as well as to classification by separating polyhedra, and to piecewise linear regression.
Cite
Text
Gottlieb et al. "Nested Barycentric Coordinate System as an Explicit Feature mAP for Polyhedra Approximation and Learning Tasks." Machine Learning, 2024. doi:10.1007/S10994-024-06596-XMarkdown
[Gottlieb et al. "Nested Barycentric Coordinate System as an Explicit Feature mAP for Polyhedra Approximation and Learning Tasks." Machine Learning, 2024.](https://mlanthology.org/mlj/2024/gottlieb2024mlj-nested/) doi:10.1007/S10994-024-06596-XBibTeX
@article{gottlieb2024mlj-nested,
title = {{Nested Barycentric Coordinate System as an Explicit Feature mAP for Polyhedra Approximation and Learning Tasks}},
author = {Gottlieb, Lee-Ad and Kaufman, Eran and Kontorovich, Aryeh and Nivasch, Gabriel and Pele, Ofir},
journal = {Machine Learning},
year = {2024},
pages = {7807-7840},
doi = {10.1007/S10994-024-06596-X},
volume = {113},
url = {https://mlanthology.org/mlj/2024/gottlieb2024mlj-nested/}
}