Novel metric for hyperbolic phylogenetic tree embeddings

Abstract

Advances in experimental technologies such as DNA sequencing have opened up new avenues for the applications of phylogenetic methods to various fields beyond their traditional application in evolutionary investigations, extending to the fields of development, differentiation, cancer genomics, and immunogenomics. Thus, the importance of phylogenetic methods is increasingly being recognized, and the development of a novel phylogenetic approach can contribute to several areas of research. Recently, the use of hyperbolic geometry has attracted attention in artificial intelligence research. Hyperbolic space can better represent a hierarchical structure compared to Euclidean space, and can therefore be useful for describing and analyzing a phylogenetic tree. In this study, we developed a novel metric that considers the characteristics of a phylogenetic tree for representation in hyperbolic space. We compared the performance of the proposed hyperbolic embeddings, general hyperbolic embeddings, and Euclidean embeddings, and confirmed that our method could be used to more precisely reconstruct evolutionary distance. We also demonstrate that our approach is useful for predicting the nearest-neighbor node in a partial phylogenetic tree with missing nodes. Furthermore, we proposed a novel approach based on our metric to integrate multiple trees for analyzing tree nodes or imputing missing distances. This study highlights the utility of adopting a geometric approach for further advancing the applications of phylogenetic methods.

Learning Hyperbolic Embedding for Phylogenetic Tree Placement and Updates

“…Related to tree embedding, Matsumoto et al [ 24 ] propose a modified version of the hyperbolic distance function to gain distance additivity for incident branches. They evaluate the performance of their method on embedding phylogenetic trees and integrating embeddings of different trees.…”

Common Methods for Phylogenetic Tree Construction and Their Implementation in R

“…Hyperbolic space has negative curvature (negative curvature: the sum of interior angles of any triangle on the surface is less than π), and its exponential expansion rate is much greater than that of Euclidean space. Therefore, compared with Euclidean embedding, hyperbolic embedding more closely matches the geometric shape of trees [115] and better represents hierarchical structures [116]. However, hyperbolic embedding is currently significantly more effective than Euclidean embedding only in low dimensions and loses its advantage in high dimensions [117].…”

Variational Bayesian phylogenies through matrix representation of tree space

“…Usually, stochastic gradient ascent is used as the optimisation algorithm, which relies on the transformation being a bijection between trees and their transformed representation. This provides a major hurdle for phylogentic inference, since existing tree spaces are either not bijective (like spanning trees between points in hyperbolic space ( Matsumoto, Mimori & Fukunaga, 2021 ; Jiang, Tabaghi & Mirarab, 2022 )) or do not allow representation as a Euclidean space (like ultrametric space ( Gavryushkin & Drummond, 2016 )).…”