Related papers: Order distances and split systems
Discrete partially ordered sets can be turned into distance spaces in several ways. The distance functions may or may not satisfy the triangle inequality, and restriction of the distance to finite chains may or may not coincide with the…
An ordered labeled tree is a tree in which the nodes are labeled and the left-to-right order among siblings is relevant. The edit distance between two ordered labeled trees is the minimum cost of changing one tree into the other through a…
Various real systems simultaneously exhibit scale-free and hierarchical structure. In this paper, we study analytically average distance in a deterministic scale-free network with hierarchical organization. Using a recursive method based on…
Kondo et al. (DS 2014) proposed methods for computing distances between unordered rooted trees by transforming an instance of the distance computing problem into an instance of the integer programming problem. They showed that the tree edit…
Clustering is a fundamental approach to understanding data patterns, wherein the intuitive Euclidean distance space is commonly adopted. However, this is not the case for implicit cluster distributions reflected by qualitative attribute…
We provide a simple method and relevant theoretical analysis for efficiently estimating higher-order lp distances. While the analysis mainly focuses on l4, our methodology extends naturally to p = 6,8,10..., (i.e., when p is even).…
Image ranking is to rank images based on some known ranked images. In this paper, we propose an improved linear ordinal distance metric learning approach based on the linear distance metric learning model. By decomposing the distance metric…
Computing the similarity between two data points plays a vital role in many machine learning algorithms. Metric learning has the aim of learning a good metric automatically from data. Most existing studies on metric learning for…
We study a family of distance functions on rankings that allow for asymmetric treatments of alternatives and consider the distinct relevance of the top and bottom positions for ordered lists. We provide a full axiomatic characterization of…
Merge trees are a common topological descriptor for data with a hierarchical component, such as terrains and scalar fields. The interleaving distance, in turn, is a common distance for comparing merge trees. However, the interleaving…
After Boltzmann and Gibbs, the notion of disorder in statistical physics relates to ensembles, not to individual states. This disorder is measured by the logarithm of ensemble volume, the entropy. But recent results about measure…
We study the problem of learning hypergraphs with shortest-path queries (SP-queries), and present the first provably optimal online algorithm for a broad and natural class of hypertrees that we call orderly hypertrees. Our online algorithm…
For $d\ge 2$ and an odd prime power $q$, consider the vector space $\mathbb{F}_q^d$ over the finite field $\mathbb{F}_q$, where the distance between two points $(x_1,\ldots,x_d)$ and $(y_1,\ldots,y_d)$ is defined as $\sum_{i=1}^d…
We consider the number of distinct distances between two finite sets of points in ${\bf R}^k$, for any constant dimension $k\ge 2$, where one set $P_1$ consists of $n$ points on a line $l$, and the other set $P_2$ consists of $m$ arbitrary…
Various real-life networks of current interest are simultaneously scale-free and modular. Here we study analytically the average distance in a class of deterministically growing scale-free modular networks. By virtue of the recursive…
We study $q$-ary codes with distance defined by a partial order of the coordinates of the codewords. Maximum Distance Separable (MDS) codes in the poset metric have been studied in a number of earlier works. We consider codes that are close…
Let \({\mathbb K}\) be any field, let \(X\subset {\mathbb P}^{k-1}\) be a set of \(n\) distinct \({\mathbb K}\)-rational points, and let \(a\geq 1\) be an integer. In this paper we find lower bounds for the minimum distance \(d(X)_a\) of…
In this article, we give a precise mathematical meaning to `linear? time' that matches experimental behaviour of the algorithm. The sorting algorithm is not our own, it is a variant of radix sort with counting sort as a subroutine. The true…
Order is one of the main instruments to measure the relationship between objects in (empirical) data. However, compared to methods that use numerical properties of objects, the amount of ordinal methods developed is rather small. One reason…
With the growing focus on semantic searches and interpretations, an increasing number of standardized vocabularies and ontologies are being designed and used to describe data. We investigate the querying of objects described by a…