Tropical Balls and Its Applications to K Nearest Neighbor over the Space of Phylogenetic Trees

Abstract

A tropical ball is a ball defined by the tropical metric over the tropical projective torus. In this paper we show several properties of tropical balls over the tropical projective torus and also over the space of phylogenetic trees with a given set of leaf labels. Then we discuss its application to the K nearest neighbors (KNN) algorithm, a supervised learning method used to classify a high-dimensional vector into given categories by looking at a ball centered at the vector, which contains K vectors in the space.

Keywords

• classification
• max-plus algebra
• phylogenomics
• ultrametrics