Related papers: Distance and Similarity Measures for Soft Sets
From last decade, when Molodtsov introduced the theory of soft set as a new approach to deal with uncertainties, until now this theory was considered sharply by a fair number of researchers. Combination of fuzzy set theory and soft set…
Finite metric spaces are the object of study in many data analysis problems. We examine the concept of weak isometry between finite metric spaces, in order to analyse properties of the spaces that are invariant under strictly increasing…
We introduce a conceptually simple and effective method to quantify the similarity between relations in knowledge bases. Specifically, our approach is based on the divergence between the conditional probability distributions over entity…
Measuring the distance between data points is fundamental to many statistical techniques, such as dimension reduction or clustering algorithms. However, improvements in data collection technologies has led to a growing versatility of…
While decision theory provides an appealing normative framework for representing rich preference structures, eliciting utility or value functions typically incurs a large cost. For many applications involving interactive systems this…
The goal of ordinal embedding is to represent items as points in a low-dimensional Euclidean space given a set of constraints in the form of distance comparisons like "item $i$ is closer to item $j$ than item $k$". Ordinal constraints like…
In this paper an idea of soft linear spaces and soft norm on soft linear spaces are given and some of their properties are studied. Soft vectors in soft linear spaces are introduced and their properties are studied. Completeness of soft…
Recently, metric learning and similarity learning have attracted a large amount of interest. Many models and optimisation algorithms have been proposed. However, there is relatively little work on the generalization analysis of such…
The objective of this manuscript is to introduce and develop the concept of a generalized $\theta$-parametric metric space-a novel extension that enriches the modern metric fixed point theory. We study of its fundamental properties,…
The semiconductor industry is one of the most technology-evolving and capital-intensive market sectors. Effective inspection and metrology are necessary to improve product yield, increase product quality and reduce costs. In recent years,…
Assessing the validity of user simulators when used for the evaluation of information retrieval systems remains an open question, constraining their effective use and the reliability of simulation-based results. To address this issue, we…
The need for appropriate ways to measure the distance or similarity between data is ubiquitous in machine learning, pattern recognition and data mining, but handcrafting such good metrics for specific problems is generally difficult. This…
In any setting in which observable properties have a quantitative flavour, it is natural to compare computational objects by way of \emph{metrics} rather than equivalences or partial orders. This holds, in particular, for probabilistic…
The paper considers a new quantitative-qualitative proximity measure for the features of information objects, where data enters a common information resource from several sources independently. The goal is to determine the possibility of…
We propose a new segmentation evaluation metric, called segmentation similarity (S), that quantifies the similarity between two segmentations as the proportion of boundaries that are not transformed when comparing them using edit distance,…
The purpose of this paper is to give a survey on the notions of distance between subsets either of a metric space or of a measure space, including definitions, a classification, and a discussion of the best-known distance functions, which…
Set functions with convenient properties (such as submodularity) appear in application areas of current interest, such as algorithmic game theory, and allow for improved optimization algorithms. It is natural to ask (e.g., in the context of…
We propose a neural network-based approach that computes a stable and generalizing metric (LSiM) to compare data from a variety of numerical simulation sources. We focus on scalar time-dependent 2D data that commonly arises from motion and…
Deep metric learning aims to learn embeddings that contain semantic similarity information among data points. To learn better embeddings, methods to generate synthetic hard samples have been proposed. Existing methods of synthetic hard…
Standardness is a popular assumption in the literature on set estimation. It also appears in statistical approaches to topological data analysis, where it is common to assume that the data were sampled from a probability measure that…