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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Tropical geometric tools for machine learning
T2 - the TML package
AU - Barnhill, D.
AU - Yoshida, R.
AU - Aliatimis, G.
AU - Miura, K.
N1 - Export Date: 30 October 2024
PY - 2024/10/5
Y1 - 2024/10/5
N2 - 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.
AB - 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.
KW - tropical data science
KW - tropical geometry
KW - tropical machine learning
U2 - 10.2140/jsag.2024.14.133
DO - 10.2140/jsag.2024.14.133
M3 - Journal article
VL - 14
SP - 133
EP - 174
JO - Journal of Software for Algebra and Geometry
JF - Journal of Software for Algebra and Geometry
IS - 1
ER -