Related papers: Distance and Similarity Measures for Soft Sets

Defining similarity measures is a requirement for some machine learning methods. One such method is case-based reasoning (CBR) where the similarity measure is used to retrieve the stored case or set of cases most similar to the query case.…

Quantifying the distance between datasets is a fundamental question in mathematics and machine learning. We propose \textit{magnitude distance}, a novel distance metric defined on finite datasets using the notion of the \emph{magnitude} of…

Representational similarity metrics typically force all units to be matched, making them susceptible to noise and outliers common in neural representations. We extend the soft-matching distance to a partial optimal transport setting that…

A quasi-metric is a distance function which satisfies the triangle inequality but is not symmetric: it can be thought of as an asymmetric metric. The central result of this thesis, developed in Chapter 3, is that a natural correspondence…

Recent work has highlighted the centrality of smooth calibration [Kakade and Foster, 2008] as a robust measure of calibration error. We generalize, unify, and extend previous results on smooth calibration, both as a robust calibration…

Distance metric learning (DML) approaches learn a transformation to a representation space where distance is in correspondence with a predefined notion of similarity. While such models offer a number of compelling benefits, it has been…

In recent years, semantic similarity measure has a great interest in Semantic Web and Natural Language Processing (NLP). Several similarity measures have been developed, being given the existence of a structured knowledge representation…

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…

Reachability analysis is at the core of many applications, from neural network verification, to safe trajectory planning of uncertain systems. However, this problem is notoriously challenging, and current approaches tend to be either too…

The growing prevalence of nonsmooth optimization problems in machine learning has spurred significant interest in generalized smoothness assumptions. Among these, the (L0, L1)-smoothness assumption has emerged as one of the most prominent.…

In this paper, we demonstrate a data-driven methodology for modelling the local similarity measures of various attributes in a dataset. We analyse the spread in the numerical attributes and estimate their distribution using polynomial…

While there has been substantial progress in learning suitable distance metrics, these techniques in general lack transparency and decision reasoning, i.e., explaining why the input set of images is similar or dissimilar. In this work, we…

A goodness-of-fit test for the fitting of a parametric model to data obtained from a detector with finite resolution and limited acceptance is proposed. The parameters of the model are found by minimization of a statistic that is used for…

The surge of research in image segmentation has yielded remarkable performance gains but also exposed a reproducibility crisis. A major contributor is performance evaluation, where both selection and implementation of metrics play critical…

In this work, we perform safety analysis of linear dynamical systems with uncertainties. Instead of computing a conservative overapproximation of the reachable set, our approach involves computing a statistical approximate reachable set. As…

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…

In an interlaboratory key comparison, a data analysis procedure for this comparison was proposed and recommended by CIPM [1, 2, 3], therein the degrees of equivalence of measurement standards of the laboratories participated in the…

Representations in the form of Symmetric Positive Definite (SPD) matrices have been popularized in a variety of visual learning applications due to their demonstrated ability to capture rich second-order statistics of visual data. There…

A measure of similarity between text embeddings can be considered adequate only if it adheres to the human perception of similarity between texts. In this paper, we introduce the distance-to-distance ratio (DDR), a novel measure of…

Today, with the emergence of semantic web technologies and increasing of information quantity, searching for information based on the semantic web has become a fertile area of research. For this reason, a large number of studies are…