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In the past few years powerful generalizations to the Euclidean k-means problem have been made, such as Bregman clustering [7], co-clustering (i.e., simultaneous clustering of rows and columns of an input matrix) [9,18], and tensor…

Quantum machine learning is one of the most promising applications of a full-scale quantum computer. Over the past few years, many quantum machine learning algorithms have been proposed that can potentially offer considerable speedups over…

\textit{Clustering problems} often arise in the fields like data mining, machine learning etc. to group a collection of objects into similar groups with respect to a similarity (or dissimilarity) measure. Among the clustering problems,…

With the rapid advances of microarray technologies, large amounts of high-dimensional gene expression data are being generated, which poses significant computational challenges. A first step towards addressing this challenge is the use of…

Data clustering is a technique for clustering set of objects into known number of groups. Several approaches are widely applied to data clustering so that objects within the clusters are similar and objects in different clusters are far…

Clustering is a usual unsupervised machine learning technique for grouping the data points into groups based upon similar features. We focus here on unsupervised clustering for contaminated data, i.e in the case where K-medians should be…

Clustering based on belief functions has been gaining increasing attention in the machine learning community due to its ability to effectively represent uncertainty and/or imprecision. However, none of the existing algorithms can be applied…

Due to the progressive growth of the amount of data available in a wide variety of scientific fields, it has become more difficult to ma- nipulate and analyze such information. Even though datasets have grown in size, the K-means algorithm…

The Euclidean k-means problem is arguably the most widely-studied clustering problem in machine learning. While the k-means objective is NP-hard in the worst-case, practitioners have enjoyed remarkable success in applying heuristics like…

In this paper, the decades-old clustering method k-means is revisited. The original distortion minimization model of k-means is addressed by a pure stochastic minimization procedure. In each step of the iteration, one sample is tentatively…

Quantum computing is a promising paradigm based on quantum theory for performing fast computations. Quantum algorithms are expected to surpass their classical counterparts in terms of computational complexity for certain tasks, including…

This paper presents a comparative analysis of different optimization techniques for the K-means algorithm in the context of big data. K-means is a widely used clustering algorithm, but it can suffer from scalability issues when dealing with…

K-means is one of the most widely used clustering algorithms in various disciplines, especially for large datasets. However the method is known to be highly sensitive to initial seed selection of cluster centers. K-means++ has been proposed…

Clustering is a popular form of unsupervised learning for geometric data. Unfortunately, many clustering algorithms lead to cluster assignments that are hard to explain, partially because they depend on all the features of the data in a…

A new procedure for simultaneously finding the optimal cluster structure of multivariate functional objects and finding the subspace to represent the cluster structure is presented. The method is based on the $k$-means criterion for…

K-Means clustering still plays an important role in many computer vision problems. While the conventional Lloyd method, which alternates between centroid update and cluster assignment, is primarily used in practice, it may converge to a…

Coresets are compact representations of data sets such that models trained on a coreset are provably competitive with models trained on the full data set. As such, they have been successfully used to scale up clustering models to massive…

In the era of big data, k-means clustering has been widely adopted as a basic processing tool in various contexts. However, its computational cost could be prohibitively high as the data size and the cluster number are large. It is well…

The $k$-means is one of the most important unsupervised learning techniques in statistics and computer science. The goal is to partition a data set into many clusters, such that observations within clusters are the most homogeneous and…

K-means is undoubtedly the most widely used partitional clustering algorithm. Unfortunately, due to its gradient descent nature, this algorithm is highly sensitive to the initial placement of the cluster centers. Numerous initialization…