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Nested barycentric coordinate system as an explicit feature map for polyhedra approximation and learning tasks
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DOI：10.1007/s10994-024-06596-x.png)
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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.
Keyword:
Feature map
Embedding
Polyhedron approximation
Function approximation
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2.9
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2.7K
被引数:
3.4W
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