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We consider the classical $k$-means clustering problem in the setting bi-criteria approximation, in which an algoithm is allowed to output $\beta k > k$ clusters, and must produce a clustering with cost at most $\alpha$ times the to the…
Offline k-means clustering was studied extensively, and algorithms with a constant approximation are available. However, online clustering is still uncharted. New factors come into play: the ordering of the dataset and whether the number of…
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…
Motivated by the fact that distances between data points in many real-world clustering instances are often based on heuristic measures, Bilu and Linial~\cite{BL} proposed analyzing objective based clustering problems under the assumption…
This paper introduces a new framework for clustering in a distributed network called Distributed Clustering based on Distributional Kernel (K) or KDC that produces the final clusters based on the similarity with respect to the distributions…
Data analysis often involves an iterative process, where solutions must be continuously refined in response to new data. Typically, as new data becomes available, an existing solution must be updated to incorporate the latest information.…
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…
Clustering categorical data is an integral part of data mining and has attracted much attention recently. In this paper, we present k-histogram, a new efficient algorithm for clustering categorical data. The k-histogram algorithm extends…
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…
Many clustering methods, including k-means, require the user to specify the number of clusters as an input parameter. A variety of methods have been devised to choose the number of clusters automatically, but they often rely on strong…
Clustering is a NP-hard problem. Thus, no optimal algorithm exists, heuristics are applied to cluster the data. Heuristics can be very resource-intensive, if not applied properly. For substantially large data sets computational efficiencies…
Cluster analysis is an unsupervised learning strategy that can be employed to identify subgroups of observations in data sets of unknown structure. This strategy is particularly useful for analyzing high-dimensional data such as microarray…
In this contribution, the clustering procedure based on K-Means algorithm is studied as an inverse problem, which is a special case of the illposed problems. The attempts to improve the quality of the clustering inverse problem drive to…
We investigate $k$-means clustering in the online no-substitution setting when the input arrives in \emph{arbitrary} order. In this setting, points arrive one after another, and the algorithm is required to instantly decide whether to take…
The goal of lifetime clustering is to develop an inductive model that maps subjects into $K$ clusters according to their underlying (unobserved) lifetime distribution. We introduce a neural-network based lifetime clustering model that can…
The $k$-center problem is a canonical and long-studied facility location and clustering problem with many applications in both its symmetric and asymmetric forms. Both versions of the problem have tight approximation factors on worst case…
A clustering may be considered as fair on pre-specified sensitive attributes if the proportions of sensitive attribute groups in each cluster reflect that in the dataset. In this paper, we consider the task of fair clustering for scenarios…
The k-means algorithm is a partitional clustering method. Over 60 years old, it has been successfully used for a variety of problems. The popularity of k-means is in large part a consequence of its simplicity and efficiency. In this paper…
The problem of constrained $k$-center clustering has attracted significant attention in the past decades. In this paper, we study balanced $k$-center cluster where the size of each cluster is constrained by the given lower and upper bounds.…
A new clustering accuracy measure is proposed to determine the unknown number of clusters and to assess the quality of clustering of a data set given in any dimensional space. Our validity index applies the classical nonparametric…