Related papers: Fixed-sized clusters $k$-Means

This paper presents universal algorithms for clustering problems, including the widely studied $k$-median, $k$-means, and $k$-center objectives. The input is a metric space containing all potential client locations. The algorithm must…

This paper introduces k-splits, an improved hierarchical algorithm based on k-means to cluster data without prior knowledge of the number of clusters. K-splits starts from a small number of clusters and uses the most significant data…

There has been considerable work on improving popular clustering algorithm `K-means' in terms of mean squared error (MSE) and speed, both. However, most of the k-means variants tend to compute distance of each data point to each cluster…

Clustering is a widely used technique with a long and rich history in a variety of areas. However, most existing algorithms do not scale well to large datasets, or are missing theoretical guarantees of convergence. This paper introduces a…

There has been much interest recently in developing fair clustering algorithms that seek to do justice to the representation of groups defined along sensitive attributes such as race and gender. We observe that clustering algorithms could…

Clustering is one of the most fundamental tools in the artificial intelligence area, particularly in the pattern recognition and learning theory. In this paper, we propose a simple, but novel approach for variance-based k-clustering tasks,…

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…

We present a study on how to effectively reduce the dimensions of the $k$-means clustering problem, so that provably accurate approximations are obtained. Four algorithms are presented, two \textit{feature selection} and two \textit{feature…

A natural way to characterize the cluster structure of a dataset is by finding regions containing a high density of data. This can be done in a nonparametric way with a kernel density estimate, whose modes and hence clusters can be found…

$\renewcommand{\Re}{{\rm I\!\hspace{-0.025em} R}} \newcommand{\eps}{{\varepsilon}} \newcommand{\Coreset}{{\mathcal{S}}} $ In this paper, we show the existence of small coresets for the problems of computing $k$-median and $k$-means…

The purpose of this paper is to improve the traditional K-means algorithm. In the traditional K mean clustering algorithm, the initial clustering centers are generated randomly in the data set. It is easy to fall into the local minimum…

Clustering is one of the most crucial problems in unsupervised learning, and the well-known $k$-means clustering algorithm has been shown to be implementable on a quantum computer with a significant speedup. However, many clustering…

Clustering algorithms have long been the topic of research, representing the more popular side of unsupervised learning. Since clustering analysis is one of the best ways to find some clarity and structure within raw data, this paper…

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…

We devise coresets for kernel $k$-Means with a general kernel, and use them to obtain new, more efficient, algorithms. Kernel $k$-Means has superior clustering capability compared to classical $k$-Means, particularly when clusters are…

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…

The $k$-means method is an iterative clustering algorithm which associates each observation with one of $k$ clusters. It traditionally employs cluster centers in the same space as the observed data. By relaxing this requirement, it is…

Finding the number of meaningful clusters in an unlabeled dataset is important in many applications. Regularized k-means algorithm is a possible approach frequently used to find the correct number of distinct clusters in datasets. The most…

The paper is focused on the forecasting method for time series groups with the use of algorithms for cluster analysis. $K$-means algorithm is suggested to be a basic one for clustering. The coordinates of the centers of clusters have been…

The clustering problem, in its many variants, has numerous applications in operations research and computer science (e.g., in applications in bioinformatics, image processing, social network analysis, etc.). As sizes of data sets have grown…