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In general, the clustering problem is NP-hard, and global optimality cannot be established for non-trivial instances. For high-dimensional data, distance-based methods for clustering or classification face an additional difficulty, the…

Statistics Theory · Mathematics 2016-04-26 Tsvetan Asamov , Adi Ben-Israel

Despite the growing popularity of explainable and interpretable machine learning, there is still surprisingly limited work on inherently interpretable clustering methods. Recently, there has been a surge of interest in explaining the…

Machine Learning · Computer Science 2024-11-26 Maximilian Fleissner , Leena Chennuru Vankadara , Debarghya Ghoshdastidar

There is growing empirical evidence that spherical $k$-means clustering performs well at identifying groups of concomitant extremes in high dimensions, thereby leading to sparse models. We provide one of the first theoretical results…

Statistics Theory · Mathematics 2022-03-21 V. Fomichov , J. Ivanovs

Cluster analysis is one of the primary data analysis technique in data mining and K-means is one of the commonly used partitioning clustering algorithm. In K-means algorithm, resulting set of clusters depend on the choice of initial…

Machine Learning · Computer Science 2015-09-11 Abhishek Kumar , Suresh Chandra Gupta

Algorithms for clustering points in metric spaces is a long-studied area of research. Clustering has seen a multitude of work both theoretically, in understanding the approximation guarantees possible for many objective functions such as…

Data Structures and Algorithms · Computer Science 2019-05-27 Maria-Florina Balcan , Travis Dick , Colin White

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

The goal of fair clustering is to find clusters such that the proportion of sensitive attributes (e.g., gender, race, etc.) in each cluster is similar to that of the entire dataset. Various fair clustering algorithms have been proposed that…

Machine Learning · Statistics 2026-02-26 Jinwon Park , Kunwoong Kim , Jihu Lee , Yongdai Kim

To cluster data that are not linearly separable in the original feature space, $k$-means clustering was extended to the kernel version. However, the performance of kernel $k$-means clustering largely depends on the choice of kernel…

Machine Learning · Computer Science 2018-11-02 Yaqiang Yao , Huanhuan Chen

Numerous papers ask how difficult it is to cluster data. We suggest that the more relevant and interesting question is how difficult it is to cluster data sets {\em that can be clustered well}. More generally, despite the ubiquity and the…

Machine Learning · Computer Science 2012-05-23 Amit Daniely , Nati Linial , Michael Saks

Clustering plays a crucial role in computer science, facilitating data analysis and problem-solving across numerous fields. By partitioning large datasets into meaningful groups, clustering reveals hidden structures and relationships within…

Databases · Computer Science 2026-02-19 Aryan Esmailpour , Stavros Sintos

In this work, we study the $k$-median and $k$-means clustering problems when the data is distributed across many servers and can contain outliers. While there has been a lot of work on these problems for worst-case instances, we focus on…

Data Structures and Algorithms · Computer Science 2019-03-08 Pranjal Awasthi , Ainesh Bakshi , Maria-Florina Balcan , Colin White , David Woodruff

The problem of rapid and automated detection of distinct market regimes is a topic of great interest to financial mathematicians and practitioners alike. In this paper, we outline an unsupervised learning algorithm for clustering financial…

Computational Finance · Quantitative Finance 2021-10-25 Blanka Horvath , Zacharia Issa , Aitor Muguruza

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

$\renewcommand{\Re}{\mathbb{R}}$Given a set $P$ of $n$ points in $\Re^d$, consider the problem of computing $k$ subsets of $P$ that form clusters that are well-separated from each other, and each of them is large (cardinality wise). We…

Computational Geometry · Computer Science 2021-06-11 Sariel Har-Peled , Joseph Rogge

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…

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…

Artificial Intelligence · Computer Science 2007-05-23 Zengyou He , Xiaofei Xu , Shengchun Deng , Bin Dong

Comparison of three kind of the clustering and find cost function and loss function and calculate them. Error rate of the clustering methods and how to calculate the error percentage always be one on the important factor for evaluating the…

Machine Learning · Computer Science 2014-11-14 Kamran Kowsari

Effectively applying the K-means algorithm to clustering tasks with incomplete features remains an important research area due to its impact on real-world applications. Recent work has shown that unifying K-means clustering and imputation…

Machine Learning · Computer Science 2025-04-14 Lovis Kwasi Armah , Igor Melnykov

We propose a new model-independent method for new physics searches called Cluster Scanning. It uses the k-means algorithm to perform clustering in the space of low-level event or jet observables, and separates potentially anomalous clusters…

High Energy Physics - Phenomenology · Physics 2024-05-22 Ivan Oleksiyuk , John Andrew Raine , Michael Krämer , Svyatoslav Voloshynovskiy , Tobias Golling

We study the problem of learning to cluster data points using an oracle which can answer same-cluster queries. Different from previous approaches, we do not assume that the total number of clusters is known at the beginning and do not…

Machine Learning · Computer Science 2021-08-18 Yi Li , Yan Song , Qin Zhang