Tropical geometric tools for machine learning : the TML package

Barnhill, D. and Yoshida, R. and Aliatimis, G. and Miura, K. (2024) Tropical geometric tools for machine learning : the TML package. Journal of Software for Algebra and Geometry, 14 (1). pp. 133-174.

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Abstract

In the last decade, developments in tropical geometry have provided a number of uses directly applicable to problems in statistical learning. The TML package is the first R package which contains a comprehensive set of tools and methods used for basic computations related to tropical convexity, visualization of tropically convex sets, as well as supervised and unsupervised learning models using the tropical metric under the max-plus algebra over the tropical projective torus. Primarily, the TML package employs a Hit-and-Run Markov chain Monte Carlo sampler in conjunction with the tropical metric as its main tool for statistical inference. In addition to basic computation and various applications of the tropical HAR sampler, we also focus on several supervised and unsupervised methods incorporated in the TML package including tropical principal component analysis, tropical logistic regression and tropical kernel density estimation.