  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 paper, 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. Finally, we define tropical SVMs over a function space with the
tropical metric and discuss the Gaussian function space as an example.
