Related papers: On Similarity
Similarity measures play a central role in various data science application domains for a wide assortment of tasks. This guide describes a comprehensive set of prevalent similarity measures to serve both non-experts and professional.…
Comparing the functional behavior of neural network models, whether it is a single network over time or two (or more networks) during or post-training, is an essential step in understanding what they are learning (and what they are not),…
An infinite class of relations between modular forms is constructed that generalizes evaluations of the Dirichlet beta function at odd positive integers. The work is motivated by a base case appearing in Ramanujan's Notebooks and a parallel…
This paper develops a theory of clustering and coding which combines a geometric model with a probabilistic model in a principled way. The geometric model is a Riemannian manifold with a Riemannian metric, ${g}_{ij}({\bf x})$, which we…
Cosmological correlators encode statistical properties of the initial conditions of our universe. Mathematically, they can often be written as Mellin integrals of a certain rational function associated to graphs, namely the flat space…
Comparative evaluation of several systems is a recurrent task in researching. It is a key step before deciding which system to use for our work, or, once our research has been conducted, to demonstrate the potential of the resulting model.…
This paper concerns the self-similarity of topological spaces, in the sense defined in math.DS/0411344. I show how to recognize self-similar spaces, or more precisely, universal solutions of self-similarity systems. Examples include the…
Similarity between objects is multi-faceted and it can be easier for human annotators to measure it when the focus is on a specific aspect. We consider the problem of mapping objects into view-specific embeddings where the distance between…
When are asymptotic approximations using the delta-method uniformly valid? We provide sufficient conditions as well as closely related necessary conditions for uniform negligibility of the remainder of such approximations. These conditions…
In this paper we generalize the famous Jacobi's triple product identity, considered as an identity for theta functions with characteristics and their derivatives, to higher genus/dimension. By applying the results and methods developed in…
In this work we extend the theory of the classical Hardy space $H^1$ to the rational Dunkl setting. Specifically, let $\Delta$ be the Dunkl Laplacian on a Euclidean space $\mathbb{R}^N$. On the half-space $\mathbb{R}_+\times\mathbb{R}^N$,…
By comparing Green functions of multi-circled plurisubharmonic singularities in the n-domensional complex space to their indicators, we obtain formulas for the higher Lelong numbers and integrability index for such singularities and extend…
ABCDE is a sophisticated technique for evaluating differences between very large clusterings. Its main metric that characterizes the magnitude of the difference between two clusterings is the JaccardDistance, which is a true distance metric…
We quantize scalar fluctuations in 1+1 dimensions above a classical background kink. The properties of the effective action for the corresponding classical field are studied with an exact functional method, alternative to exact Wilsonian…
A self-contained discussion of integral equations of scattering is presented in the case of centrally-symmetric potentials in one dimension, which will facilitate the understanding of more complex scattering integral equations in two and…
The primary objective of the present paper is to develop the theory of quantization dimension of an invariant measure associated with an iterated function system consisting of finite number of contractive infinitesimal similitudes in a…
We introduce a basis of the symmetric functions that evaluates to the (irreducible) characters of the symmetric group, just as the Schur functions evaluate to the irreducible characters of $GL_n$ modules. Our main result gives three…
Inequalities are established for certain trilinear scalar-valued functionals. These functionals act on measurable functions of one real variable, are defined by integration over two- or three-dimensional spaces, and are controlled in terms…
The use of correntropy as a similarity measure has been increasing in different scenarios due to the well-known ability to extract high-order statistic information from data. Recently, a new similarity measure between complex random…
We study two new families of symmetric functions arising from a species-theoretic construction motivated by cycle structure. For each partition of $n$, we define two combinatorial species that decompose into molecules indexed by the same…