Related papers: Rough families, cluster points, and cores
Unlike on images, semantic learning on 3D point clouds using a deep network is challenging due to the naturally unordered data structure. Among existing works, PointNet has achieved promising results by directly learning on point sets.…
This paper studies the fair range clustering problem in which the data points are from different demographic groups and the goal is to pick $k$ centers with the minimum clustering cost such that each group is at least minimally represented…
The aim of the present paper is to extend the concept of a congruence from lattices to posets. We use an approach different from that used by the first author and V. Sn\'a\v{s}el. By using our definition we show that congruence classes are…
X-ray clusters are powerful tools for the determination of cosmological parameters. More specifically, the combined knowledge of the redshift distribution of X-ray clusters together with the luminosity-temperature correlation, $L_X-T_X$…
Clustering is one of the most fundamental problems in data analysis and it has been studied extensively in the literature. Though many clustering algorithms have been proposed, clustering theories that justify the use of these clustering…
We study supervised learning problems using clustering constraints to impose structure on either features or samples, seeking to help both prediction and interpretation. The problem of clustering features arises naturally in text…
Superclusters are a convenient way to partition and characterize the large scale structure of the Universe. In this Letter we explore the advantages of defining superclusters as watershed basins in the divergence velocity field. We apply…
Constrained clustering is a semi-supervised task that employs a limited amount of labelled data, formulated as constraints, to incorporate domain-specific knowledge and to significantly improve clustering accuracy. Previous work has…
Designing small-sized \emph{coresets}, which approximately preserve the costs of the solutions for large datasets, has been an important research direction for the past decade. We consider coreset construction for a variety of general…
The main purpose of this paper is to introduce and study minimal and maximal ideals defined on ideal topological spaces. Also, we define and investigate the concepts of ideal quotient and annihilator of any subfamily of $2^X$, where $2^X$…
A topological group $X$ is called connected if the only subsets which are both open and closed are the whole space $X$ and the null set $\emptyset$. A subset of a topological group is connected if the subspace is connected. We say that a…
Clusters or communities can provide a coarse-grained description of complex systems at multiple scales, but their detection remains challenging in practice. Community detection methods often define communities as dense subgraphs, or…
We study the possible growth rates of the Kolmogorov complexity of initial segments of sequences that are random with respect to some computable measure on $2^\omega$, the so-called proper sequences. Our main results are as follows: (1) We…
Community and core-periphery are two widely studied graph structures, with their coexistence observed in real-world graphs (Rombach, Porter, Fowler \& Mucha [SIAM J. App. Math. 2014, SIAM Review 2017]). However, the nature of this…
Clustering with outliers is one of the most fundamental problems in Computer Science. Given a set $X$ of $n$ points and two integers $k$ and $m$, the clustering with outliers aims to exclude $m$ points from $X$ and partition the remaining…
Correlation clustering is a concept of machine learning. The ultimate goal of such a clustering is to find a partition with minimal conflicts. In this paper we investigate a correlation clustering of integers, based upon the greatest common…
We introduce the notion of ideally supported achievement sets for a series of real numbers. We analize their complexity and topological properties. We compare the notion of ideal achievement sets with the notion of ideally supported sum…
Coresets have become an invaluable tool for solving $k$-means and kernel $k$-means clustering problems on large datasets with small numbers of clusters. On the other hand, spectral clustering works well on sparse graphs and has recently…
Fault-tolerant complexes describe surface-code fault-tolerant protocols from a single geometric object. We first introduce fusion complexes that define a general family of fusion-based quantum computing (FBQC) fault-tolerant quantum…
We consider the coset poset associated with the families of proper subgroups, proper subgroups of finite index, and proper normal subgroups of finite index. We investigate under which conditions those coset posets have contractible…