Related papers: Recognizing and realizing cactus metrics
The emergence of massive graph data sets requires fast mining algorithms. Centrality measures to identify important vertices belong to the most popular analysis methods in graph mining. A measure that is gaining attention is forest…
A new method of metric space investigation, based on classification of its finite subspaces, is suggested. It admits to derive information on metric space properties which is encoded in metric. The method describes geometry in terms of only…
In recent years, considerable advances have been made in the study of properties of metric spaces in terms of their doubling dimension. This line of research has not only enhanced our understanding of finite metrics, but has also resulted…
This paper introduces \textit{measurement trees}, a novel class of metrics designed to combine various constructs into an interpretable multi-level representation of a measurand. Unlike conventional metrics that yield single values,…
A phylogenetic tree shows the evolutionary relationships among species. Internal nodes of the tree represent speciation events and leaf nodes correspond to species. A goal of phylogenetics is to combine such trees into larger trees, called…
We study the conditions under which the isometry of spaces with metrics generated by weights given on the edges of finite trees is equivalent to the isomorphism of these trees. Similar questions are studied for ultrametric spaces generated…
We propose a new graph metric and study its properties. In contrast to the standard distance in connected graphs, it takes into account all paths between vertices. Formally, it is defined as d(i,j)=q_{ii}+q_{jj}-q_{ij}-q_{ji}, where q_{ij}…
Important data mining problems such as nearest-neighbor search and clustering admit theoretical guarantees when restricted to objects embedded in a metric space. Graphs are ubiquitous, and clustering and classification over graphs arise in…
A graph $G=(V,E)$ with geodesic distance $d(\cdot,\cdot)$ is said to be resolved by a non-empty subset $R$ of its vertices when, for all vertices $u$ and $v$, if $d(u,r)=d(v,r)$ for each $r\in R$, then $u=v$. The metric dimension of $G$ is…
A vertex set $U \subseteq V$ of an undirected graph $G=(V,E)$ is a $\textit{resolving set}$ for $G$, if for every two distinct vertices $u,v \in V$ there is a vertex $w \in U$ such that the distances between $u$ and $w$ and the distance…
Reachability is the problem of deciding whether there is a path from one vertex to the other in the graph. Standard graph traversal algorithms such as DFS and BFS take linear time to decide reachability however their space complexity is…
A metric phylogenetic tree relating a collection of taxa induces weighted rooted triples and weighted quartets for all subsets of three and four taxa, respectively. New intertaxon distances are defined that can be calculated from these…
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…
Fitting distances to tree metrics and ultrametrics are two widely used methods in hierarchical clustering, primarily explored within the context of numerical taxonomy. Given a positive distance function…
The performance of graph algorithms is often measured in terms of the number of traversed edges per second (TEPS). However, this performance metric is inadequate for a graph operation such as exact triangle counting. In triangle counting,…
Similarity search is an important problem in information retrieval. This similarity is based on a distance. Symbolic representation of time series has attracted many researchers recently, since it reduces the dimensionality of these high…
There is a rising interest in mapping trees using satellite or aerial imagery, but there is no standardized evaluation protocol for comparing and enhancing methods. In dense canopy areas, the high variability of tree sizes and their spatial…
We study the problem of supervised learning a metric space under discriminative constraints. Given a universe $X$ and sets ${\cal S}, {\cal D}\subset {X \choose 2}$ of similar and dissimilar pairs, we seek to find a mapping $f:X\to Y$, into…
Nonlinear metrics, such as the F1-score, Matthews correlation coefficient, and Fowlkes-Mallows index, are often used to evaluate the performance of machine learning models, in particular, when facing imbalanced datasets that contain more…
Different types of two- and three-dimensional representations of a finite metric space are studied that focus on the accurate representation of the linear order among the distances rather than their actual values. Lower and upper bounds for…