Related papers: Is the Chen-Sbert Divergence a Metric?
Jensen-Shannon divergence is a well known multi-purpose measure of dissimilarity between probability distributions. It has been proven that the square root of this quantity is a true metric in the sense that, in addition to the basic…
This paper contains bounds for the distortion in the spherical metric, that is to say bounds for the constant of Holder continuity of mappings f : (\Rn,q) -> (\Rn, q) where q denotes the spherical metric. The mappings considered are…
In this paper, the concept of the classical $f$-divergence (for a pair of measures) is extended to the mixed $f$-divergence (for multiple pairs of measures). The mixed $f$-divergence provides a way to measure the difference between multiple…
This work studies the Geometric Jensen-Shannon divergence, based on the notion of geometric mean of probability measures, in the setting of Gaussian measures on an infinite-dimensional Hilbert space. On the set of all Gaussian measures…
In this paper, the concept of the classical $f$-divergence for a pair of measures is extended to the mixed $f$-divergence for multiple pairs of measures. The mixed $f$-divergence provides a way to measure the difference between multiple…
We explore the notion of degree of asymmetry for integer sequences and related combinatorial objects. The degree of asymmetry is a new combinatorial statistic that measures how far an object is from being symmetric. We define this notion…
We propose a family of near-metrics based on local graph diffusion to capture similarity for a wide class of data sets. These quasi-metametrics, as their names suggest, dispense with one or two standard axioms of metric spaces, specifically…
We consider two independent and stationary measures over $\chi^\mathbb{N}$, where $\chi$ finite or countable alphabet. For each pair of $n$-strings in the product space we define $T_n^{(2)}$ as the length of the shortest path connecting one…
We show that Lelek's problem on the chainability of continua with span zero is not a metric problem: from a non-metric counterexample one can construct a metric one.
Several measures exist for string similarity, including notable ones like the edit distance and the indel distance. The former measures the count of insertions, deletions, and substitutions required to transform one string into another,…
This paper deals with three major types of convergence of probability measures on metric spaces: weak convergence, setwise converges, and convergence in the total variation. First, it describes and compares necessary and sufficient…
While recent work has established divergence as a key framework for understanding evenness, there is currently no research exploring how the families of measures within the divergence-based framework relate to each other. This paper uses…
A binary word is symmetric if it is a palindrome or an antipalindrome. We define a new measure of asymmetry of a binary word equal to the minimal number of letters of the word whose deleting from the word yields a symmetric word and obtain…
A set of n non-collinear points in the Euclidean plane defines at least n different lines. Chen and Chv\'tal in 2008 conjectured that the same results is true in metric spaces for an adequate definition of line. More recently, it was…
The metric dimension of a general metric space was defined in 1953, applied to the set of vertices of a graph metric in 1975, and developed further for metric spaces in 2013. It was then generalised in 2015 to the k-metric dimension of a…
We propose a new definition of the chi-square divergence between distributions. Based on convexity properties and duality, this version of the {\chi}^2 is well suited both for the classical applications of the {\chi}^2 for the analysis of…
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…
For a non-negative function $\psi: ~ \N \mapsto \R$, let $W(\psi)$ denote the set of real numbers $x$ for which the inequality $|n x - a| < \psi(n)$ has infinitely many coprime solutions $(a,n)$. The Duffin--Schaeffer conjecture, one of the…
A subgraph $H$ of a graph $G$ is isometric if the distances between vertices in $H$ coincide with the distances between the corresponding vertices in $G$. We show that for any integer $n\ge 1$, there is a graph on $3^{n+O(\log^2 n)}$…
In a recent paper, the generalization of the Jensen Shannon divergence (JSD) in the context of quantum theory has been studied (Phys. Rev. A 72, 052310 (2005)). This distance between quantum states has shown to verify several of the…