Related papers: Universal Similarity
Dimension is a fundamental property of objects and the space in which they are embedded. Yet ideal notions of dimension, as in Euclidean spaces, do not always translate to physical spaces, which can be constrained by boundaries and…
We begin with pervasive ultrametricity due to high dimensionality and/or spatial sparsity. How extent or degree of ultrametricity can be quantified leads us to the discussion of varied practical cases when ultrametricity can be partially or…
We give an overview of different approaches to measuring the similarity of, or the distance between, two graphs, highlighting connections between these approaches. We also discuss the complexity of computing the distances.
A distance measure is presented between two unitary propagators of quantum systems of differing dimensions along with a corresponding method of computation. A typical application is to compare the propagator of the actual (real) process…
Compatibility between items, such as clothes and shoes, is a major factor among customer's purchasing decisions. However, learning "compatibility" is challenging due to (1) broader notions of compatibility than those of similarity, (2) the…
This paper is about similarity between objects that can be represented as points in metric measure spaces. A metric measure space is a metric space that is also equipped with a measure. For example, a network with distances between its…
Data uniformity is a concept associated with several semantic data characteristics such as lack of features, correlation and sample bias. This article introduces a novel measure to assess data uniformity and detect uniform pointsets on…
The widespread relevance of complex networks is a valuable tool in the analysis of a broad range of systems. There is a demand for tools which enable the extraction of meaningful information and allow the comparison between different…
The study of the topological structure of complex networks has fascinated researchers for several decades, and today we have a fairly good understanding of the types and reoccurring characteristics of many different complex networks.…
The ability to mimic human notions of semantic distance has widespread applications. Some measures rely only on raw text (distributional measures) and some rely on knowledge sources such as WordNet. Although extensive studies have been…
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…
Quantifying the degree of similarity between images is a key copyright issue for image-based machine learning. In legal doctrine however, determining the degree of similarity between works requires subjective analysis, and fact-finders…
Given a set of sequences, the distance between pairs of them helps us to find their similarity and derive structural relationship amongst them. For genomic sequences such measures make it possible to construct the evolution tree of…
Measuring the similarity of images is a fundamental problem to computer vision for which no universal solution exists. While simple metrics such as the pixel-wise L2-norm have been shown to have significant flaws, they remain popular. One…
We survey permutation-based methods for approximate k-nearest neighbor search. In these methods, every data point is represented by a ranked list of pivots sorted by the distance to this point. Such ranked lists are called permutations. The…
In pattern recognition, learning, and data mining one obtains information from information-carrying objects. This involves an objective definition of the information in a single object, the information to go from one object to another…
Crowdsourced, or human computation based clustering algorithms usually rely on relative distance comparisons, as these are easier to elicit from human workers than absolute distance information. A relative distance comparison is a statement…
The paper considers various formalisms based on Automata, Temporal Logic and Regular Expressions for specifying queries over sequences. Unlike traditional binary semantics, the paper presents a similarity based semantics for thse…
We analytically study proximity and distance properties of various kernels and similarity measures on graphs. This helps to understand the mathematical nature of such measures and can potentially be useful for recommending the adoption of…
The Levenshtein distance is an important tool for the comparison of symbolic sequences, with many appearances in genome research, linguistics and other areas. For efficient applications, an approximation by a distance of smaller…