Related papers: Rough families, cluster points, and cores
In this paper, we formulate the problem of inferring a Finite Mixture Model from discrete data as an optimal transport problem with entropic regularization of parameter $\lambda\geq 0$. Our method unifies hard and soft clustering, the…
A novel and intuitive nearest neighbours based clustering algorithm is introduced, in which a cluster is defined in terms of an equilibrium condition which balances its size and cohesiveness. The formulation of the equilibrium condition…
Necessary and sufficient conditions for the exactness (in the algebraic sense) of certain sequences of continuous group homomorphisms are established.
In this paper we define the closure under weak convergence of the class of p-tempered {\alpha}-stable distributions. We give necessary and sufficient conditions for convergence of sequences in this class. Moreover, we show that any element…
The concept of I-statistical convergence of a double sequence was first introduced and study by Das et. el [2]. Here in this paper we discuss some results on rough ideal statistical convergence and also we introduce the notion of rough…
A relational structure is a core, if all its endomorphisms are embeddings. This notion is important for computational complexity classification of constraint satisfaction problems. It is a fundamental fact that every finite structure has a…
We continue the study of cluster algebras initiated in math.RT/0104151 and math.RA/0208229. We develop a new approach based on the notion of an upper cluster algebra, defined as an intersection of certain Laurent polynomial rings.…
A \emph{strong coreset} for the mean queries of a set $P$ in ${\mathbb{R}}^d$ is a small weighted subset $C\subseteq P$, which provably approximates its sum of squared distances to any center (point) $x\in {\mathbb{R}}^d$. A \emph{weak…
An ideal $I$ is a family of subsets of positive integers $\textbf{N}$ which is closed under taking finite unions and subsets of its elements. A sequence $(x_n)$ of real numbers is said to be $I$-convergent to a real number $L$, if for each…
Graph clustering is the problem of identifying sparsely connected dense subgraphs (clusters) in a given graph. Proposed clustering algorithms usually optimize various fitness functions that measure the quality of a cluster within the graph.…
Coresets have emerged as a powerful tool to summarize data by selecting a small subset of the original observations while retaining most of its information. This approach has led to significant computational speedups but the performance of…
Originally, tangles were invented as an abstract tool in mathematical graph theory to prove the famous graph minor theorem. In this paper, we showcase the practical potential of tangles in machine learning applications. Given a collection…
We deal with the problem of semantic classification of challenging and highly-cluttered dataset. We present a novel, and yet a very simple classification technique by leveraging the ease of classifiability of any existing well separable…
Coreset of a given dataset and loss function is usually a small weighed set that approximates this loss for every query from a given set of queries. Coresets have shown to be very useful in many applications. However, coresets construction…
Cluster analysis requires many decisions: the clustering method and the implied reference model, the number of clusters and, often, several hyper-parameters and algorithms' tunings. In practice, one produces several partitions, and a final…
We present convergence theory for corrected quadrature rules on uniform Cartesian grids for functions with a point singularity. We begin by deriving an error estimate for the punctured trapezoidal rule, and then derive error expansions. We…
A coreset is a small set that can approximately preserve the structure of the original input data set. Therefore we can run our algorithm on a coreset so as to reduce the total computational complexity. Conventional coreset techniques…
Clustering is an important part of many modern data analysis pipelines, including network analysis and data retrieval. There are many different clustering algorithms developed by various communities, and it is often not clear which…
Given an ideal $\mathcal{I}$ on the nonnegative integers $\omega$ and a Polish space $X$, let $\mathscr{L}(\mathcal{I})$ be the family of subsets $S\subseteq X$ such that $S$ is the set of $\mathcal{I}$-limit points of some sequence taking…
We give sufficient conditions for a group of homeomorphisms of a Peano continuum X without cut-points to be a convergence group. The condition is that there is a collection of convergence subgroups whose limit sets `cut up' X in the correct…