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 language||English GB|
|Title of host publication||Proceedings of The 24th International Conference on Artificial Intelligence and Statistics|
|Editors||Arindam Banerjee, Kenji Fukumizu|
|Number of pages||9|
|State||Published - 2021|
|Name||Proceedings of Machine Learning Research|