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We propose a new embedding method which is particularly well-suited forsettings where the sample size greatly exceeds the ambient dimension. Ourtechnique consists of partitioning the space into simplices and then embeddingthe data points into features corresponding to the simplices' barycentriccoordinates. We then train a linear classifier in the rich feature spaceobtained from the simplices. The decision boundary may be highly non-linear,though it is linear within each simplex (and hence piecewise-linear overall).Further, our method can approximate any convex body. We give generalizationbounds based on empirical margin and a novel hybrid sample compressiontechnique. An extensive empirical evaluation shows that our method consistentlyoutperforms a range of popular kernel embedding methods.

Nested Barycentric Coordinate System as an Explicit Feature Map