Related papers: Computational Feasibility of Clustering under Clus…

It is well known that most of the common clustering objectives are NP-hard to optimize. In practice, however, clustering is being routinely carried out. One approach for providing theoretical understanding of this seeming discrepancy is to…

Numerous papers ask how difficult it is to cluster data. We suggest that the more relevant and interesting question is how difficult it is to cluster data sets {\em that can be clustered well}. More generally, despite the ubiquity and the…

Clustering is an essential data mining tool that aims to discover inherent cluster structure in data. For most applications, applying clustering is only appropriate when cluster structure is present. As such, the study of clusterability,…

Clustering is a fundamental data mining tool that aims to divide data into groups of similar items. Generally, intuition about clustering reflects the ideal case -- exact data sets endowed with flawless dissimilarity between individual…

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…

One basic requirement of many studies is the necessity of classifying data. Clustering is a proposed method for summarizing networks. Clustering methods can be divided into two categories named model-based approaches and algorithmic…

Cluster analysis has attracted more and more attention in the field of machine learning and data mining. Numerous clustering algorithms have been proposed and are being developed due to diverse theories and various requirements of emerging…

In recent years, much of the research on clustering algorithms has primarily focused on enhancing their accuracy and efficiency, frequently at the expense of interpretability. However, as these methods are increasingly being applied in…

Clustering uncertain data has emerged as a challenging task in uncertain data management and mining. Thanks to a computational complexity advantage over other clustering paradigms, partitional clustering has been particularly studied and a…

Clustering is an essential data mining tool that aims to discover inherent cluster structure in data. As such, the study of clusterability, which evaluates whether data possesses such structure, is an integral part of cluster analysis. Yet,…

We study the problem of explainability-first clustering where explainability becomes a first-class citizen for clustering. Previous clustering approaches use decision trees for explanation, but only after the clustering is completed. In…

Clustering algorithms aim to organize data into groups or clusters based on the inherent patterns and similarities within the data. They play an important role in today's life, such as in marketing and e-commerce, healthcare, data…

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…

We introduce a novel criterion in clustering that seeks clusters with limited range of values associated with each cluster's elements. In clustering or classification the objective is to partition a set of objects into subsets, called…

This paper studies the computational difficulty of clustering problems that are defined directly on a continuous probability density. Rather than working with finite samples, we assume the density is given as a polynomial and ask whether it…

Many social networks and complex systems are found to be naturally divided into clusters of densely connected nodes, known as community structure (CS). Finding CS is one of fundamental yet challenging topics in network science. One of the…

A computational theory for clustering and a semi-supervised clustering algorithm is presented. Clustering is defined to be the obtainment of groupings of data such that each group contains no anomalies with respect to a chosen grouping…

Recently, there has been substantial interest in clustering research that takes a beyond worst-case approach to the analysis of algorithms. The typical idea is to design a clustering algorithm that outputs a near-optimal solution, provided…

Many clustering schemes are defined by optimizing an objective function defined on the partitions of the underlying set of a finite metric space. In this paper, we construct a framework for studying what happens when we instead impose…

Numerous algorithms have been produced for the fundamental problem of clustering under many different notions of fairness. Perhaps the most common family of notions currently studied is group fairness, in which proportional group…