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Related papers: Min-Sum Clustering (with Outliers)

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We consider the problem of principal component analysis (PCA) in the presence of outliers. Given a matrix $A$ ($d \times n$) and parameters $k, m$, the goal is to remove a set of at most $m$ columns of $A$ (known as outliers), so as to…

Data Structures and Algorithms · Computer Science 2018-05-14 Aditya Bhaskara , Srivatsan Kumar

A well-known bottleneck of Min-Sum-of-Square Clustering (MSSC, the celebrated $k$-means problem) is to tackle the presence of outliers. In this paper, we propose a Partial clustering variant termed PMSSC which considers a fixed number of…

Computational Complexity · Computer Science 2023-06-01 Nicolas Dupin , Frank Nielsen

In this paper we propose a graph-based data clustering algorithm which is based on exact clustering of a minimum spanning tree in terms of a minimum isoperimetry criteria. We show that our basic clustering algorithm runs in $O(n \log n)$…

Computer Vision and Pattern Recognition · Computer Science 2012-03-20 Amir Daneshgar , Ramin Javadi , Basir Shariat Razavi

Recently, there has been substantial interest in clustering research that takes a beyond worst-case approach to the analysis of algorithms. The typical idea is to design a clustering algorithm that outputs a near-optimal solution, provided…

Data Structures and Algorithms · Computer Science 2018-12-31 Maria-Florina Balcan , Colin White

A data filtering method for cluster analysis is proposed, based on minimizing a least squares function with a weighted $\ell_0$-norm penalty. To overcome the discontinuity of the objective function, smooth non-convex functions are employed…

Optimization and Control · Mathematics 2017-05-23 Andrea Cristofari

We study a clustering problem where the goal is to maximize the coverage of the input points by $k$ chosen centers. Specifically, given a set of $n$ points $P \subseteq \mathbb{R}^d$, the goal is to pick $k$ centers $C \subseteq…

Computational Geometry · Computer Science 2020-04-14 Arturs Backurs , Sariel Har-Peled

Clustering, or unsupervised classification, is a task often plagued by outliers. Yet there is a paucity of work on handling outliers in clustering. Outlier identification algorithms tend to fall into three broad categories: outlier…

Methodology · Statistics 2024-05-31 Katharine M. Clark , Paul D. McNicholas

Clustering is a fundamental tool in data mining. It partitions points into groups (clusters) and may be used to make decisions for each point based on its group. However, this process may harm protected (minority) classes if the clustering…

Data Structures and Algorithms · Computer Science 2018-11-27 Ioana O. Bercea , Martin Groß , Samir Khuller , Aounon Kumar , Clemens Rösner , Daniel R. Schmidt , Melanie Schmidt

In this paper we consider clustering problems in which each point is endowed with a color. The goal is to cluster the points to minimize the classical clustering cost but with the additional constraint that no color is over-represented in…

Data Structures and Algorithms · Computer Science 2019-05-31 Sara Ahmadian , Alessandro Epasto , Ravi Kumar , Mohammad Mahdian

We consider the problem of approximate $K$-means clustering with outliers and side information provided by same-cluster queries and possibly noisy answers. Our solution shows that, under some mild assumptions on the smallest cluster size,…

Machine Learning · Statistics 2018-11-13 I Chien , Chao Pan , Olgica Milenkovic

We introduce and study the $k$-center clustering problem with set outliers, a natural and practical generalization of the classical $k$-center clustering with outliers. Instead of removing individual data points, our model allows discarding…

Data Structures and Algorithms · Computer Science 2025-12-23 Vaishali Surianarayanan , Neeraj Kumar , Stavros Sintos

We propose a simple and efficient clustering method for high-dimensional data with a large number of clusters. Our algorithm achieves high-performance by evaluating distances of datapoints with a subset of the cluster centres. Our…

Machine Learning · Computer Science 2022-03-30 Georgios Exarchakis , Omar Oubari , Gregor Lenz

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

The objective of clustering is to discover natural groups in datasets and to identify geometrical structures which might reside there, without assuming any prior knowledge on the characteristics of the data. The problem can be seen as…

Computational Geometry · Computer Science 2018-01-26 Luis-Evaristo Caraballo , José-Miguel Díaz-Báñez , Nadine Kroher

\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,…

Computational Geometry · Computer Science 2015-12-10 Sayan Bandyapadhyay , Kasturi Varadarajan

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…

Machine Learning · Computer Science 2020-09-23 Sanjoy Dasgupta , Nave Frost , Michal Moshkovitz , Cyrus Rashtchian

This paper introduces {\em fusion subspace clustering}, a novel method to learn low-dimensional structures that approximate large scale yet highly incomplete data. The main idea is to assign each datum to a subspace of its own, and minimize…

Machine Learning · Computer Science 2022-05-24 Usman Mahmood , Daniel Pimentel-Alarcón

The problem of clustering a set of points moving on the line consists of the following: given positive integers n and k, the initial position and the velocity of n points, find an optimal k-clustering of the points. We consider two…

Computational Geometry · Computer Science 2015-12-23 Cristina G. Fernandes , Marcio T. I. Oshiro

We resolve a long-standing open question, about the existence of a constant-factor approximation algorithm for the average-case \textsc{Decision Tree} problem with uniform probability distribution over the hypotheses. We answer the question…

Data Structures and Algorithms · Computer Science 2026-04-29 Michał Szyfelbein

Clustering is a fundamental task in data mining and machine learning, particularly for analyzing large-scale data. In this paper, we introduce Clust-Splitter, an efficient algorithm based on nonsmooth optimization, designed to solve the…

Machine Learning · Computer Science 2026-03-19 Jenni Lampainen , Kaisa Joki , Napsu Karmitsa , Marko M. Mäkelä