Related papers: Order distances and split systems
In the infinite regular tree $\mathbb{T}_{q+1}$ with $q \in \mathbb{Z}_{\ge 2}$, we consider families $\{\mu_u^n\}$, indexed by vertices $u$ and nonnegative integers ("discrete time steps") $n$, of probability measures such that $\mu_u^n(v)…
Distance queries are a basic tool in data analysis. They are used for detection and localization of change for the purpose of anomaly detection, monitoring, or planning. Distance queries are particularly useful when data sets such as…
Resistance distance computation is a fundamental problem in graph analysis, yet existing random walk-based methods are limited to approximate solutions and suffer from poor efficiency on small-treewidth graphs (e.g., road networks). In…
Characterization of medium-range order in amorphous materials and its relation to short-range order is discussed. A new topological approach is presented here to extract a hierarchical structure of amorphous materials, which is robust…
We introduce and analyze Structured Stochastic Zeroth order Descent (S-SZD), a finite difference approach that approximates a stochastic gradient on a set of $l\leq d$ orthogonal directions, where $d$ is the dimension of the ambient space.…
First we consider pair-wise distances for literal objects consisting of finite binary files. These files are taken to contain all of their meaning, like genomes or books. The distances are based on compression of the objects concerned,…
Regularized discrete optimal transport (OT) is a powerful tool to measure the distance between two discrete distributions that have been constructed from data samples on two different domains. While it has a wide range of applications in…
Circuity, the ratio of network distances to straight-line distances, is an important measure of urban street network structure and transportation efficiency. Circuity results from a circulation network's configuration, planning, and…
The axiomatic analysis of IR evaluation metrics has contributed to a better understanding of their properties. Some works have modelled the effectiveness of retrieval measures with axioms that capture desirable properties on the set of…
To overcome computational challenges of Optimal Transport (OT), several variants of Sliced Wasserstein (SW) has been developed in the literature. These approaches exploit the closed-form expression of the univariate OT by projecting…
Graphs and complex networks can be successively separated into connected components associated to respective seed nodes, therefore establishing a respective hierarchical organization. In the present work, we study the properties of the…
This article describes a new system for induction of oblique decision trees. This system, OC1, combines deterministic hill-climbing with two forms of randomization to find a good oblique split (in the form of a hyperplane) at each node of a…
This paper is devoted to a systematic study of a class of binary trees encoding the structure of rational numbers both from arithmetic and dynamical point of view. The paper is divided into two parts. The first one is a critical review of…
Given two distributions $\mathcal{P}$ and $\mathcal{Q}$ over a high-dimensional domain $\{0,1\}^n$, and a parameter $\varepsilon$, the goal of distance estimation is to determine the statistical distance between $\mathcal{P}$ and…
Two kinds of evolving trees are considered here: the exponential trees, where subsequent nodes are linked to old nodes without any preference, and the Barab\'asi--Albert scale-free networks, where the probability of linking to a node is…
A causal set is a partially ordered set on a countably infinite ground-set such that each element is above finitely many others. A natural extension of a causal set is an enumeration of its elements which respects the order. We bring…
We determine the distributions of lengths of runs in random sequences of elements from a totally ordered set (total order) or partially ordered set (partial order). In particular, we produce novel formulae for the expected value, variance,…
The matrices of spanning rooted forests are studied as a tool for analysing the structure of networks and measuring their properties. The problems of revealing the basic bicomponents, measuring vertex proximity, and ranking from preference…
We investigate a relationship network of humans located in a metric space where relationships are drawn according to a distance-dependent probability density. The obtained spatial graph allows us to calculate the average separation of…
In the $L_0$ Fitting Tree Metrics problem, we are given all pairwise distances among the elements of a set $V$ and our output is a tree metric on $V$. The goal is to minimize the number of pairwise distance disagreements between the input…