Tropical neural networks and its applications to classifying phylogenetic trees
Loading...
Authors
Yoshida, Ruriko
Aliatimis, Georgios
Miura, Keiji
Subjects
Advisors
Date of Issue
2023-09-26
Date
September 23, 2023
Publisher
ArXiv
Language
Abstract
Deep neural networks show great success when input vectors are in an
Euclidean space. However, those classical neural networks show a poor
performance when inputs are phylogenetic trees, which can be written
as vectors in the tropical projective torus. Here we propose tropical embedding to transform a vector in the tropical projective torus to a vector
in the Euclidean space via the tropical metric. We introduce a tropical
neural network where the first layer is a tropical embedding layer and
the following layers are the same as the classical ones. We prove that
this neural network with the tropical metric is a universal approximator
and we derive a backpropagation rule for deep neural networks. Then we
provide TensorFlow 2 codes for implementing a tropical neural network
in the same fashion as the classical one, where the weights initialization
problem is considered according to the extreme value statistics. We apply our method to empirical data including sequences of hemagglutinin
for influenza virus from New York. Finally, we show that a tropical neural network can be interpreted as a generalization of a tropical logistic
regression.
Type
Preprint
Description
The article of record as published may be found at https://arxiv.org/abs/2309.13410
Series/Report No
Department
Organization
Naval Postgraduate School
Identifiers
NPS Report Number
Sponsors
Funder
Format
21 p.
Citation
Yoshida, Ruriko, Georgios Aliatimis, and Keiji Miura. "Tropical neural networks and its applications to classifying phylogenetic trees." arXiv preprint arXiv:2309.13410 (2023).
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.