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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…

Data Structures and Algorithms · Computer Science 2020-10-01 Pankaj K. Agarwal , Hsien-Chih Chang , Kamesh Munagala , Erin Taylor , Emo Welzl

This paper investigates the validity of Kleinberg's axioms for clustering functions with respect to the quite popular clustering algorithm called $k$-means. While Kleinberg's axioms have been discussed heavily in the past, we concentrate…

Machine Learning · Computer Science 2017-04-25 Robert Kłopotek , Mieczysław Kłopotek

This paper proposes a new distance metric between clusterings that incorporates information about the spatial distribution of points and clusters. Our approach builds on the idea of a Hilbert space-based representation of clusters as a…

Machine Learning · Computer Science 2015-03-18 Parasaran Raman , Jeff M. Phillips , Suresh Venkatasubramanian

We consider the problem of subspace clustering: given points that lie on or near the union of many low-dimensional linear subspaces, recover the subspaces. To this end, one first identifies sets of points close to the same subspace and uses…

Machine Learning · Statistics 2014-11-03 Dohyung Park , Constantine Caramanis , Sujay Sanghavi

We study the task of differentially private clustering. For several basic clustering problems, including Euclidean DensestBall, 1-Cluster, k-means, and k-median, we give efficient differentially private algorithms that achieve essentially…

Machine Learning · Computer Science 2020-08-19 Badih Ghazi , Ravi Kumar , Pasin Manurangsi

Clustering methods such as k-means have found widespread use in a variety of applications. This paper proposes a formal testing procedure to determine whether a null hypothesis of a single cluster, indicating homogeneity of the data, can be…

Econometrics · Economics 2019-07-18 Andrew J. Patton , Brian M. Weller

Clustering is a classic topic in optimization with $k$-means being one of the most fundamental such problems. In the absence of any restrictions on the input, the best known algorithm for $k$-means with a provable guarantee is a simple…

Data Structures and Algorithms · Computer Science 2017-04-11 Sara Ahmadian , Ashkan Norouzi-Fard , Ola Svensson , Justin Ward

Centroid based clustering methods such as k-means, k-medoids and k-centers are heavily applied as a go-to tool in exploratory data analysis. In many cases, those methods are used to obtain representative centroids of the data manifold for…

Machine Learning · Computer Science 2022-06-16 Ahmed Imtiaz Humayun , Randall Balestriero , Anastasios Kyrillidis , Richard Baraniuk

Notwithstanding the popularity of conventional clustering algorithms such as K-means and probabilistic clustering, their clustering results are sensitive to the presence of outliers in the data. Even a few outliers can compromise the…

Machine Learning · Statistics 2015-05-27 Pedro A. Forero , Vassilis Kekatos , Georgios B. Giannakis

While K-means is known to be a standard clustering algorithm, its performance may be compromised due to the presence of outliers and high-dimensional noisy variables. This paper proposes adaptively robust and sparse K-means clustering…

Computation · Statistics 2024-11-08 Hao Li , Shonosuke Sugasawa , Shota Katayama

This work explores the clustering of wireless users by examining the distances between their channel covariance matrices, which reside on the Riemannian manifold of positive definite matrices. Specifically, we consider an estimator of the…

Signal Processing · Electrical Eng. & Systems 2024-08-09 Roberto Pereira , Xavier Mestre

Sparse clustering, which aims to find a proper partition of an extremely high-dimensional data set with redundant noise features, has been attracted more and more interests in recent years. The existing studies commonly solve the problem in…

Machine Learning · Statistics 2019-02-25 Xiangyu Chang , Yu Wang , Rongjian Li , Zongben Xu

k-means has recently been recognized as one of the best algorithms for clustering unsupervised data. Since k-means depends mainly on distance calculation between all data points and the centers, the time cost will be high when the size of…

Data Structures and Algorithms · Computer Science 2011-08-08 Raied Salman , Vojislav Kecman , Qi Li , Robert Strack , Erik Test

Recent spectral clustering methods are a propular and powerful technique for data clustering. These methods need to solve the eigenproblem whose computational complexity is $O(n^3)$, where $n$ is the number of data samples. In this paper, a…

Machine Learning · Computer Science 2007-11-26 Chunjing Xu , Jianzhuang Liu , Xiaoou Tang

K-means clustering is widely used in psychological and psychometric research to identify profiles, subgroups, and potential typologies, yet its classical formulation does not test whether such groups exist as latent psychological…

There is a long history of research into time series clustering using distance-based partitional clustering. Many of the most popular algorithms adapt k-means (also known as Lloyd's algorithm) to exploit time dependencies in the data by…

Machine Learning · Computer Science 2024-10-21 Christopher Holder , Anthony Bagnall , Jason Lines

This paper studies clustering of data sequences using the k-medoids algorithm. All the data sequences are assumed to be generated from \emph{unknown} continuous distributions, which form clusters with each cluster containing a composite set…

Machine Learning · Computer Science 2019-03-27 Tiexing Wang , Qunwei Li , Donald J. Bucci , Yingbin Liang , Biao Chen , Pramod K. Varshney

Clustering methods are a valuable tool for the identification of patterns in high dimensional data with applications in many scientific problems. However, quantifying uncertainty in clustering is a challenging problem, particularly when…

Methodology · Statistics 2018-06-01 Marcio Valk , Gabriela Bettella Cybis

Spherical k-means is a widely used clustering algorithm for sparse and high-dimensional data such as document vectors. While several improvements and accelerations have been introduced for the original k-means algorithm, not all easily…

Machine Learning · Computer Science 2021-11-02 Erich Schubert , Andreas Lang , Gloria Feher

Clustering is one of the most important unsupervised problems in machine learning and statistics. Among many existing algorithms, kernel k-means has drawn much research attention due to its ability to find non-linear cluster boundaries and…

Machine Learning · Statistics 2016-12-05 Bowei Yan , Purnamrita Sarkar