Related papers: On Similarity
This paper presents a new similarity measure to be used for general tasks including supervised learning, which is represented by the K-nearest neighbor classifier (KNN). The proposed similarity measure is invariant to large differences in…
In this paper, we revisit pattern mining and study the distribution underlying a binary dataset thanks to the closure structure which is based on passkeys, i.e., minimum generators in equivalence classes robust to noise. We introduce…
The scattering cross section associated with a two dimensional delta function has recently been the object of considerable study. It is shown here that this problem can be put into a field theoretical framework by the construction of an…
New analytical expressions are found for the Levi-Civita symbol using the Kronecker delta symbol. The expressions are derived up to 3 dimensions, extended to higher dimensions, and confirmed in Matlab for 5 dimensions. The expressions can…
: In studies of discrete structures, functions are frequently used that express proximity, but are not metrics. We consider a class of such functions that is characterized by a normalization condition and an inequality that plays the same…
Quantifying the similarity between datasets has widespread applications in statistics and machine learning. The performance of a predictive model on novel datasets, referred to as generalizability, depends on how similar the training and…
Dirac delta function (delta-distribution) approach can be used as efficient method to derive identities for number series and their reciprocals. Applying this method, a simple proof for identity relating prime counting function…
We study universal approximation of continuous functionals on compact subsets of products of Hilbert spaces. We prove that any such functional can be uniformly approximated by models that first take finitely many continuous linear…
We analyze different approaches to differential-algebraic equations with attention to the implemented rank conditions of various matrix functions. These conditions are apparently very different and certain rank drops in some matrix…
Using an algorithm for computing the symmetric function Kronecker product of D-finite symmetric functions we find some new Kronecker product identities. The identities give closed form formulas for trace-like values of the Kronecker…
I continue the investigation of a q-analogue of the convolution on the line started in a joint work with Koornwinder and based on a formal definition due to Kempf and Majid. Two different ways of approximating functions by means of the…
Vector similarity measures play a fundamental role in various fields, including machine learning, natural language processing, information retrieval, and data mining. These measures quantify the closeness between two vectors in a…
Measuring inter-dataset similarity is an important task in machine learning and data mining with various use cases and applications. Existing methods for measuring inter-dataset similarity are computationally expensive, limited, or…
for representing, characterizing, and modeling an ample range of structures and phenomena from both theoretical and applied perspectives. The present work describes the application of the recently introduced real-valued Jaccard and…
In this paper, the asymptotic distributions of estimators for the regularized functional canonical correlation and variates of the population are derived. The method is based on the possibility of expressing these regularized quantities as…
In this work we describe and compare the classic inner product and Pearson correlation coefficient as well as the recently introduced real-valued Jaccard and coincidence indices. Special attention is given to diverse schemes for taking into…
Let $d_{\alpha, \beta}(n)=\sum\limits_{\substack{n=kl \alpha l<k\leq\beta l}}1$ be the number of ways of factoring n into two almost equal integers. For rational numbers $0<\alpha <\beta $, we consider the following Zeta function…
The Dirac delta function is widely used in many areas of physics and mathematics. Here we consider the generalization of a Dirac delta function to allow the use of complex arguments. We show that the properties of a generalized delta…
In classical canonical correlation analysis (CCA), the goal is to determine the linear transformations of two random vectors into two new random variables that are most strongly correlated. Canonical variables are pairs of these new random…
Methods for quantifying the similarity of datasets are relevant in applications where two or more datasets, or their underlying distributions, need to be compared, ranging from two- and k-sample testing to applications in machine learning…