Related papers: Separated Red Blue Center Clustering

We consider the $k$-center problem in which the centers are constrained to lie on two lines. Given a set of $n$ weighted points in the plane, we want to locate up to $k$ centers on two parallel lines. We present an $O(n\log^2 n)$ time…

We consider online $k$-means clustering where each new point is assigned to the nearest cluster center, after which the algorithm may update its centers. The loss incurred is the sum of squared distances from new points to their assigned…

In the non-uniform $k$-center problem, the objective is to cover points in a metric space with specified number of balls of different radii. Chakrabarty, Goyal, and Krishnaswamy [ICALP 2016, Trans. on Algs. 2020] (CGK, henceforth) give a…

We present an $(e^{O(p)} \frac{\log \ell}{\log\log\ell})$-approximation algorithm for socially fair clustering with the $\ell_p$-objective. In this problem, we are given a set of points in a metric space. Each point belongs to one (or…

We propose a new algorithm for k-means clustering in a distributed setting, where the data is distributed across many machines, and a coordinator communicates with these machines to calculate the output clustering. Our algorithm guarantees…

We study the problem of fairness in k-centers clustering on data with disjoint demographic groups. Specifically, this work proposes a variant of fairness which restricts each group's number of centers with both a lower bound…

The Johnson-Lindenstrauss (JL) Lemma introduced the concept of dimension reduction via a random linear map, which has become a fundamental technique in many computational settings. For a set of $n$ points in $\mathbb{R}^d$ and any fixed…

This paper studies the problem of clustering in metric spaces while preserving the privacy of individual data. Specifically, we examine differentially private variants of the k-medians and Euclidean k-means problems. We present polynomial…

Center-based clustering is a pivotal primitive for unsupervised learning and data analysis. A popular variant is undoubtedly the k-means problem, which, given a set $P$ of points from a metric space and a parameter $k<|P|$, requires to…

$k$-means clustering is a fundamental problem in unsupervised learning. The problem concerns finding a partition of the data points into $k$ clusters such that the within-cluster variation is minimized. Despite its importance and wide…

In this paper, the decades-old clustering method k-means is revisited. The original distortion minimization model of k-means is addressed by a pure stochastic minimization procedure. In each step of the iteration, one sample is tentatively…

We investigate $k$-means clustering in the online no-substitution setting when the input arrives in \emph{arbitrary} order. In this setting, points arrive one after another, and the algorithm is required to instantly decide whether to take…

Given a stream of points in a metric space, is it possible to maintain a constant approximate clustering by changing the cluster centers only a small number of times during the entire execution of the algorithm? This question received…

This paper considers a canonical clustering problem where one receives unlabeled samples drawn from a balanced mixture of two elliptical distributions and aims for a classifier to estimate the labels. Many popular methods including PCA and…

In this work, we study the socially fair $k$-median/$k$-means problem. We are given a set of points $P$ in a metric space $\mathcal{X}$ with a distance function $d(.,.)$. There are $\ell$ groups: $P_1,\dotsc,P_{\ell} \subseteq P$. We are…

In the past few years powerful generalizations to the Euclidean k-means problem have been made, such as Bregman clustering [7], co-clustering (i.e., simultaneous clustering of rows and columns of an input matrix) [9,18], and tensor…

We study the problem of clustering ranking vectors, where each vector represents preferences as an ordered list of distinct integers. Specifically, we focus on the k-centroids ranking vectors clustering problem (KRC), which aims to…

Clustering is a fundamental problem in many scientific applications. Standard methods such as $k$-means, Gaussian mixture models, and hierarchical clustering, however, are beset by local minima, which are sometimes drastically suboptimal.…

The minimum sum-of-squares clustering (MSSC), or k-means type clustering, is traditionally considered an unsupervised learning task. In recent years, the use of background knowledge to improve the cluster quality and promote…

We propose a new variant of the k-median problem, where the objective function models not only the cost of assigning data points to cluster representatives, but also a penalty term for disagreement among the representatives. We motivate…