2023/09/23 by Ruriko Yoshida, Yoshida, Ruriko, Georgios Aliatimis +3
Biochemistry, Genetics and Molecular Biology · #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Genomics and Phylogenetic Studies #Machine Learning in Bioinformatics
paper · pdf · doi:10.48550/arxiv.2309.13410
openalex publication_date 2023/09/23 · openalex created_date 2023/09/27 · openalex updated_date 2026/07/28
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.