Related papers: Intrinsic Interleaving Distance for Merge Trees
We consider the problem of estimating species trees from unrooted gene tree topologies in the presence of incomplete lineage sorting, a common phenomenon that creates gene tree heterogeneity in multilocus datasets. One popular class of…
We propose a statistical method to test whether two phylogenetic trees with given alignments are significantly incongruent. Our method compares the two distributions of phylogenetic trees given by the input alignments, instead of comparing…
Metric graphs are special types of metric spaces used to model and represent simple, ubiquitous, geometric relations in data such as biological networks, social networks, and road networks. We are interested in giving a qualitative…
The rapid advancement of large language models (LLMs) has enabled significant strides in various fields. This paper introduces a novel approach to evaluate the effectiveness of LLM embeddings in the context of inherent geometric properties.…
An added edge to a graph is called an inset edge. Predicting k inset edges which minimize the average distance of a graph is known to be NP-Hard. However, when k = 1 the complexity of the problem is polynomial. In this paper, some tools for…
Using the wedge sum of metric spaces, for all compact metrizable spaces, we construct a topological embedding of the compact metrizable space into the set of all metric trees in the Gromov--Hausdorff space with finite prescribed values. As…
Tropical geometry with the max-plus algebra has been applied to statistical learning models over tree spaces because geometry with the tropical metric over tree spaces has some nice properties such as convexity in terms of the tropical…
In order to conduct a statistical analysis on a given set of phylogenetic gene trees, we often use a distance measure between two trees. In a statistical distance-based method to analyze discordance between gene trees, it is a key to decide…
Minimal spanning trees on infinite vertex sets are investigated. A criterion for minimality of a spanning tree having a finite length is obtained, which generalizes the corresponding classical result for finite sets. It is given an analytic…
Optimal transport provides a metric which quantifies the dissimilarity between probability measures. For measures supported in discrete metric spaces, finding the optimal transport distance has cubic time complexity in the size of the…
In this paper, we study the joint behaviour of the degree, depth and label of and graph distance between high-degree vertices in the random recursive tree. We generalise the results obtained by Eslava and extend these to include the labels…
A labeled metric space is intuitively speaking a metric space together with a special set of points to be understood as the geometric boundary of the space. We study basic properties of a recently introduced labeled Gromov-Hausdorff…
An added edge to a graph is called an inset edge. Predicting k inset edges which minimize the average distance of a graph is known to be NP-Hard. When k = 1 the complexity of the problem is polynomial. In this paper, we further find the…
This work briefly explores the possibility of approximating spatial distance (alternatively, similarity) between data points using the Isolation Forest method envisioned for outlier detection. The logic is similar to that of isolation: the…
The problem of comparing trees representing the evolutionary histories of cancerous tumors has turned out to be crucial, since there is a variety of different methods which typically infer multiple possible trees. A departure from the…
Understanding the response of an output variable to multi-dimensional inputs lies at the heart of many data exploration endeavours. Topology-based methods, in particular Morse theory and persistent homology, provide a useful framework for…
The log-det distance between two aligned DNA sequences was introduced as a tool for statistically consistent inference of a gene tree under simple non-mixture models of sequence evolution. Here we prove that the log-det distance, coupled…
The search for similarity and dissimilarity measures on phylogenetic trees has been motivated by the computation of consensus trees, the search by similarity in phylogenetic databases, and the assessment of clustering results in…
We define, analyze, and give efficient algorithms for two kinds of distance measures for rooted and unrooted phylogenies. For rooted trees, our measures are based on the topologies the input trees induce on triplets; that is, on…
We address the problem of merging graph and feature-space information while learning a metric from structured data. Existing algorithms tackle the problem in an asymmetric way, by either extracting vectorized summaries of the graph…