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We generalize finite-sample bounds for convex clustering to the setting where affinity weights appearing in the objective correspond to a general connected graph. These bounds and their analysis lead to a better understanding of clustering…

Machine Learning · Statistics 2026-05-26 Sam Rosen , Jason Xu

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…

Data Structures and Algorithms · Computer Science 2021-07-16 Arun Ganesh , Bruce M. Maggs , Debmalya Panigrahi

A novel nonparametric clustering algorithm is proposed using the interpoint distances between the members of the data to reveal the inherent clustering structure existing in the given set of data, where we apply the classical nonparametric…

Methodology · Statistics 2024-09-02 Soumita Modak

The reconstruction of galaxy cluster's gas density profiles is usually performed by assuming spherical symmetry and averaging the observed X-ray emission in circular annuli. In the case of a very inhomogeneous and asymmetric gas…

Cosmology and Nongalactic Astrophysics · Physics 2017-03-15 D. Eckert , M. Roncarelli , S. Ettori , S. Molendi , F. Vazza , F. Gastaldello , M. Rossetti

In recent years, spectral clustering has become a standard method for data analysis used in a broad range of applications. In this paper we propose a new class of algorithms for multiway spectral clustering based on optimization of a…

Machine Learning · Computer Science 2016-05-05 James Voss , Mikhail Belkin , Luis Rademacher

Given a point set S and an unknown metric d on S, we study the problem of efficiently partitioning S into k clusters while querying few distances between the points. In our model we assume that we have access to one versus all queries that…

Machine Learning · Computer Science 2014-08-12 Konstantin Voevodski , Maria-Florina Balcan , Heiko Roglin , Shang-Hua Teng , Yu Xia

In the planted partition problem, the $n$ vertices of a random graph are partitioned into $k$ "clusters," and edges between vertices in the same cluster and different clusters are included with constant probability $p$ and $q$, respectively…

Data Structures and Algorithms · Computer Science 2017-08-24 Sam Cole

In this paper we initiate a systematic study of exact algorithms for well-known clustering problems, namely $k$-Median and $k$-Means. In $k$-Median, the input consists of a set $X$ of $n$ points belonging to a metric space, and the task is…

Data Structures and Algorithms · Computer Science 2022-08-16 Fedor V. Fomin , Petr A. Golovach , Tanmay Inamdar , Nidhi Purohit , Saket Saurabh

Classical multidimensional scaling is an important dimension reduction technique. Yet few theoretical results characterizing its statistical performance exist. This paper provides a theoretical framework for analyzing the quality of…

Statistics Theory · Mathematics 2020-07-09 Anna Little , Yuying Xie , Qiang Sun

Current catalogues of open clusters are rather heterogeneous and incomplete lists of clusters than true catalogues. Before there has been no attempts of automatic search for open clusters in huge photometric catalogues using homogeneous…

Astrophysics · Physics 2007-05-23 Ivan Zolotukhin , Sergey Koposov , Elena Glushkova

A direct approach to studying the galaxy-halo connection is to analyze groups and clusters of galaxies that trace the underlying dark matter halos, emphasizing the importance of identifying galaxy clusters and their associated brightest…

Cosmology and Nongalactic Astrophysics · Physics 2025-01-22 Hai-Xia Ma , Tsutomu T. Takeuchi , Suchetha Cooray , Yongda Zhu

Convex clustering is an attractive clustering algorithm with favorable properties such as efficiency and optimality owing to its convex formulation. It is thought to generalize both k-means clustering and agglomerative clustering. However,…

Machine Learning · Statistics 2021-05-19 Canh Hao Nguyen , Hiroshi Mamitsuka

Clustered standard errors and approximate randomization tests are popular inference methods that allow for dependence within observations. However, they require researchers to know the cluster structure ex ante. We propose a procedure to…

Econometrics · Economics 2022-01-14 Yong Cai

Convex clustering has recently garnered increasing interest due to its attractive theoretical and computational properties, but its merits become limited in the face of high-dimensional data. In such settings, pairwise affinity terms that…

Methodology · Statistics 2021-04-02 Saptarshi Chakraborty , Jason Xu

We use the galaxy cluster X-ray temperature distribution function to constrain the amplitude of the power spectrum of density inhomogeneities on the scale corresponding to clusters. We carry out the analysis for critical density universes,…

Astrophysics · Physics 2015-06-24 Pedro T P Viana , Andrew R Liddle

k-medoids algorithm is a partitional, centroid-based clustering algorithm which uses pairwise distances of data points and tries to directly decompose the dataset with $n$ points into a set of $k$ disjoint clusters. However, k-medoids…

Machine Learning · Computer Science 2015-12-15 Mehrdad Ghadiri , Amin Aghaee , Mahdieh Soleymani Baghshah

Suppose, we are given a set of $n$ elements to be clustered into $k$ (unknown) clusters, and an oracle/expert labeler that can interactively answer pair-wise queries of the form, "do two elements $u$ and $v$ belong to the same cluster?".…

Machine Learning · Statistics 2017-06-26 Arya Mazumdar , Barna Saha

Motivated by many applications, we study clustering with a faulty oracle. In this problem, there are $n$ items belonging to $k$ unknown clusters, and the algorithm is allowed to ask the oracle whether two items belong to the same cluster or…

Machine Learning · Computer Science 2022-07-13 Jinghui Xia , Zengfeng Huang

In this paper, we propose a family of label recovery problems on weighted Euclidean random graphs. The vertices of a graph are embedded in $\mathbb{R}^d$ according to a Poisson point process, and are assigned to a discrete community label.…

Social and Information Networks · Computer Science 2025-01-15 Julia Gaudio , Charlie Guan , Xiaochun Niu , Ermin Wei

Density based spatial clustering of points in $\mathbb{R}^n$ has a myriad of applications in a variety of industries. We generalise this problem to the density based clustering of lines in high-dimensional spaces, keeping in mind there…

Machine Learning · Computer Science 2024-10-04 Akanksha Das , Malay Bhattacharyya