Related papers: The Normalized Edit Distance with Uniform Operatio…
Quantifying the similarity between two graphs is a fundamental algorithmic problem at the heart of many data analysis tasks for graph-based data. In this paper, we study the computational complexity of a family of similarity measures based…
We propose a simple real-valued generalization of the well known integer-valued Erdos number as a topological, non-metric measure of the `closeness' felt between two nodes in an undirected, weighted graph. These real-valued Erdos numbers…
The Optimal transport (OT) problem is rapidly finding its way into machine learning. Favoring its use are its metric properties. Many problems admit solutions with guarantees only for objects embedded in metric spaces, and the use of…
The edit distance between two strings is defined as the smallest number of insertions, deletions, and substitutions that need to be made to transform one of the strings to another one. Approximating edit distance in subquadratic time is…
We consider approximating a measure by a parameterized curve subject to length penalization. That is for a given finite positive compactly supported measure $\mu$, for $p \geq 1$ and $\lambda>0$ we consider the functional \[ E(\gamma) =…
This paper introduces a new mathematical formulation and numerical approach for the computation of distances and geodesics between immersed planar curves. Our approach combines the general simplifying transform for first-order elastic…
We solve the problem of best approximation by partial isometries of given rank to an arbitrary rectangular matrix, when the distance is measured in any unitarily invariant norm. In the case where the norm is strictly convex, we parametrize…
This article demonstrates how a large number of efficiency measures known in the literature in production economics can be interpreted through the notion of utility function, based on the concept of Stone-Geary utility. Several…
In this paper, we study the metric distortion of deterministic social choice rules that choose a winning candidate from a set of candidates based on voter preferences. Voters and candidates are located in an underlying metric space. A voter…
The tree edit distance is a natural dissimilarity measure between rooted ordered trees whose nodes are labeled over an alphabet $\Sigma$. It is defined as the minimum number of node edits (insertions, deletions, and relabelings) required to…
Document alignment techniques based on multilingual sentence representations have recently shown state of the art results. However, these techniques rely on unsupervised distance measurement techniques, which cannot be fined-tuned to the…
Computing the edit distance of two strings is one of the most basic problems in computer science and combinatorial optimization. Tree edit distance is a natural generalization of edit distance in which the task is to compute a measure of…
Metric dimensions and metric basis are graph invariants studied for their use in locating and indexing nodes in a graph. It was recently established that for bicyclic graph of type-III ($\Theta $-graphs), the metric dimension is $3$ only,…
The dynamic time warping (dtw) distance fails to satisfy the triangle inequality and the identity of indiscernibles. As a consequence, the dtw-distance is not warping-invariant, which in turn results in peculiarities in data mining…
The goal of this note is to provide a geometric setting in which generalized arithmetic means are best predictors in an appropriate metric. This characterization provides a geometric interpretation to the concept of certainty equivalent.…
We develop an inferential toolkit for analyzing object-valued responses, which correspond to data situated in general metric spaces, paired with Euclidean predictors within the conformal framework. To this end we introduce conditional…
We compare the profit of the optimal third-degree price discrimination policy against a uniform pricing policy. A uniform pricing policy offers the same price to all segments of the market. Our main result establishes that for a broad class…
In the field of statistical disclosure control, the tradeoff between data confidentiality and data utility is measured by comparing disclosure risk and information loss metrics. Distance based metrics such as the mean absolute error (MAE),…
Metric embeddings are a widely used method in algorithm design, where generally a ``complex'' metric is embedded into a simpler, lower-dimensional one. Historically, the theoretical computer science community has focused on bi-Lipschitz…
We study the average edit distance between two random strings. More precisely, we adapt a technique introduced by Lueker in the context of the average longest common subsequence of two random strings to improve the known upper bound on the…