TItle: Tropical Support Vector Machines

Abstract:  Support Vector Machines (SVMs) are one of the most popular supervised learning models to classify using a hyperplane in an Euclidean space. Similar to SVMs, tropical SVMs classify data points using a tropical hyperplane under the tropical metric with the max-plus algebra. In this talk, first we show generalization error bounds of tropical SVMs over the tropical projective space. While the generalization error bounds attained via VC dimensions in a distribution-free manner still depend on the dimension, we also show theoretically by extreme value statistics that the tropical SVMs for classifying data points from two Gaussian distributions as well as empirical data sets of different neuron types are fairly robust against the curse of dimensionality. Extreme value statistics also underlie the anomalous scaling behaviors of the tropical distance between random vectors with additional noise dimensions.  This is joint work with M. Takamori, H. Matsumoto and K. Miura.