Related papers: The k-outlier Fr\'echet distance
k-means has recently been recognized as one of the best algorithms for clustering unsupervised data. Since k-means depends mainly on distance calculation between all data points and the centers, the time cost will be high when the size of…
Big data mining is well known to be an important task for data science, because it can provide useful observations and new knowledge hidden in given large datasets. Proximity-based data analysis is particularly utilized in many real-life…
It is well known, that Fr\'echet means on non-Euclidean spaces may exhibit nonstandard asymptotic rates depending on curvature. Even for distributions featuring standard asymptotic rates, there are non-Euclidean effects, altering finite…
Sliced Wasserstein distances are widely used in practice as a computationally efficient alternative to Wasserstein distances in high dimensions. In this paper, motivated by theoretical foundations of this alternative, we prove quantitative…
Biological processes like growth, aging, and disease progression are generally studied with follow-up scans taken at different time points, i.e., with image time series (TS) based analysis. Comparison between TS representing a biological…
We describe a $O(\log n )$-approximation algorithm for computing the homotopic \Frechet distance between two polygonal curves that lie on the boundary of a triangulated topological disk. Prior to this work, algorithms were known only for…
In this paper, we present a novel two-stage metric learning algorithm. We first map each learning instance to a probability distribution by computing its similarities to a set of fixed anchor points. Then, we define the distance in the…
In data analysis, there is a strong demand for graph metrics that differ from the classical shortest path and resistance distances. Recently, several new classes of graph metrics have been proposed. This paper presents some of them…
In this paper, we revisit the notion of length measures associated to planar closed curves. These are a special case of area measures of hypersurfaces which were introduced early on in the field of convex geometry. The length measure of a…
In this paper we consider several variants of the pattern matching problem. In particular, we investigate the following problems: 1) Pattern matching with k mismatches; 2) Approximate counting of mismatches; and 3) Pattern matching with…
We prove that the length difference between a closed periodic curve and its parallel curve at a sufficiently small distance is proportional to the rotation index. As an application, the rotation index of a curve could be estimated by means…
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…
The distance function $\varrho(p,q)$ (or $d(p,q)$) of a distance space (general metric space) is not differentiable in general. We investigate such distance spaces over $\mathbb R^n$, whose distance functions are differentiable like in case…
We study the problem of sub-trajectory nearest-neighbor queries on polygonal curves under the continuous Fr\'echet distance. Given an $n$ vertex trajectory $P$ and an $m$ vertex query trajectory $Q$, we seek to report a vertex-aligned…
The Vapnik-Chervonenkis dimension provides a notion of complexity for systems of sets. If the VC dimension is small, then knowing this can drastically simplify fundamental computational tasks such as classification, range counting, and…
Distances are fundamental primitives whose choice significantly impacts the performances of algorithms in machine learning and signal processing. However selecting the most appropriate distance for a given task is an endeavor. Instead of…
Distances on merge trees facilitate visual comparison of collections of scalar fields. Two desirable properties for these distances to exhibit are 1) the ability to discern between scalar fields which other, less complex topological…
Distance covariance and distance correlation have been widely adopted in measuring dependence of a pair of random variables or random vectors. If the computation of distance covariance and distance correlation is implemented directly…
To solve the problems in measuring coefficient of skewness related to extreme value, irregular distance from the middle point and distance between two consecutive numbers, "Rank skewness" a new measure of the coefficient of skewness has…
Alternative novel measures of the distance between any two partitions of a n-set are proposed and compared, together with a main existing one, namely 'partition-distance' D(.,.). The comparison achieves by checking their restriction to…