Related papers: Clustering Stability: An Overview

We consider the problem of center-based clustering in low-dimensional Euclidean spaces under the perturbation stability assumption. An instance is $\alpha$-stable if the underlying optimal clustering continues to remain optimal even when…

A theory of clustering of inertial particles advected by a turbulent velocity field caused by an instability of their spatial distribution is suggested. The reason for the clustering instability is a combined effect of the particles inertia…

We develop a probabilistic method for assessing the tail behavior and geometric stability of one-dimensional n i.i.d. samples by tracking how their span contracts when the most extreme points are trimmed. Central to our approach is the…

Suppose a researcher observes individuals within a county within a state. Given concerns about correlation across individuals, it is common to group observations into clusters and conduct inference treating observations across clusters as…

The clustering of a data set is one of the core tasks in data analytics. Many clustering algorithms exhibit a strong contrast between a favorable performance in practice and bad theoretical worst-cases. Prime examples are least-squares…

In this research, a general theoretical framework for clustering is proposed over specific partial algebraic systems by the present author. Her theory helps in isolating minimal assumptions necessary for different concepts of clustering…

We suggested a theory of clustering of inertial particles advected by a turbulent velocity field caused by an instability of their spatial distribution. The reason of the {\em clustering instability} is a combined effect of the particle…

In this paper we consider clustering problems in which each point is endowed with a color. The goal is to cluster the points to minimize the classical clustering cost but with the additional constraint that no color is over-represented in…

Most research on predicting community evolution focuses on changes in the states of communities. Instead, we focus on individual nodes and define the novel problem of predicting whether a specific node stays in the same cluster, moves to…

Using a measure of clustering derived from the nearest neighbour distribution and the void probability function we are able to distinguish between regular and clustered structures. With an example we show that regularity is a property of a…

Cluster analysis has become one of the most exercised research areas over the past few decades in computer science. As a consequence, numerous clustering algorithms have already been developed to find appropriate partitions of a set of…

Unsupervised learning is widely recognized as one of the most important challenges facing machine learning nowa- days. However, in spite of hundreds of papers on the topic being published every year, current theoretical understanding and…

Star clusters are ideal tracers of star formation activity in systems outside the volume that can be studied using individual, resolved stars. These unresolved clusters span orders of magnitude in brightness and mass, and their formation is…

Motivated by data on coauthorships in scientific publications, we analyze a team formation process that generalizes matching models and network formation models, allowing for overlapping teams of heterogeneous size. We apply different…

Despite its popularity, it is widely recognized that the investigation of some theoretical aspects of clustering has been relatively sparse. One of the main reasons for this lack of theoretical results is surely the fact that, whereas for…

Clustering aims to group unlabeled objects based on similarity inherent among them into clusters. It is important for many tasks such as anomaly detection, database sharding, record linkage, and others. Some clustering methods are taken as…

Clustering is part of unsupervised analysis methods that consist in grouping samples into homogeneous and separate subgroups of observations also called clusters. To interpret the clusters, statistical hypothesis testing is often used to…

When scholars suspect units are dependent on each other within clusters but independent of each other across clusters, they employ cluster-robust standard errors (CRSEs). Nevertheless, what to cluster over is sometimes unknown. For…

A solid observational characterization of cluster regions around the virial radius would allow us to improve considerably our understanding of the physics of galaxy clusters as a whole: sadly current and planned experiments will not allow…

Recently, many regularized procedures have been proposed for variable selection in linear regression, but their performance depends on the tuning parameter selection. Here a criterion for the tuning parameter selection is proposed, which…