相关论文: $k$-center Clustering under Perturbation Resilienc…

Given a set of points, clustering consists of finding a partition of a point set into $k$ clusters such that the center to which a point is assigned is as close as possible. Most commonly, centers are points themselves, which leads to the…

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…

Clustering problems have numerous applications and are becoming more challenging as the size of the data increases. In this paper, we consider designing clustering algorithms that can be used in MapReduce, the most popular programming…

In this paper, we consider the fault-tolerant $k$-median problem and give the \emph{first} constant factor approximation algorithm for it. In the fault-tolerant generalization of classical $k$-median problem, each client $j$ needs to be…

The K-means algorithm is one of the most widely studied clustering algorithms in machine learning. While extensive research has focused on its ability to achieve a globally optimal solution, there still lacks a rigorous analysis of its…

We consider stochastic settings for clustering, and develop provably-good approximation algorithms for a number of these notions. These algorithms yield better approximation ratios compared to the usual deterministic clustering setting.…

A set of points $P$ in a metric space and a constant integer $k$ are given. The $k$-center problem finds $k$ points as centers among $P$, such that the maximum distance of any point of $P$ to their closest centers $(r)$ is minimized.…

We consider robust clustering problems in $\mathbb{R}^d$, specifically $k$-clustering problems (e.g., $k$-Median and $k$-Means with $m$ outliers, where the cost for a given center set $C \subset \mathbb{R}^d$ aggregates the distances from…

A fair clustering instance is given a data set $A$ in which every point is assigned some color. Colors correspond to various protected attributes such as sex, ethnicity, or age. A fair clustering is an instance where membership of points in…

In [SIAM J. Optim., 2022], the authors introduced a new linear programming (LP) relaxation for K-means clustering. In this paper, we further investigate both theoretical and computational properties of this relaxation. As evident from our…

Metric $k$-center clustering is a fundamental unsupervised learning primitive. Although widely used, this primitive is heavily affected by noise in the data, so that a more sensible variant seeks for the best solution that disregards a…

In this paper, we present a new iterative rounding framework for many clustering problems. Using this, we obtain an $(\alpha_1 + \epsilon \leq 7.081 + \epsilon)$-approximation algorithm for $k$-median with outliers, greatly improving upon…

Metric based comparison operations such as finding maximum, nearest and farthest neighbor are fundamental to studying various clustering techniques such as $k$-center clustering and agglomerative hierarchical clustering. These techniques…

Aiming to unify known results about clustering mixtures of distributions under separation conditions, Kumar and Kannan[2010] introduced a deterministic condition for clustering datasets. They showed that this single deterministic condition…

Persistent homology is a methodology central to topological data analysis that extracts and summarizes the topological features within a dataset as a persistence diagram; it has recently gained much popularity from its myriad successful…

The fairness of clustering algorithms has gained widespread attention across various areas, including machine learning, In this paper, we study fair $k$-means clustering in Euclidean space. Given a dataset comprising several groups, the…

Clustering is a widely used unsupervised learning method for finding structure in the data. However, the resulting clusters are typically presented without any guarantees on their robustness; slightly changing the used data sample or…

The sum of radii problem ($k$-MSR) asks, given a metric space on $n$ points, to place $k$ balls covering all points so as to minimize the sum of their radii. Despite extensive study from the perspectives of approximation and parameterized…

The p-center problem consists in selecting p facilities from a set of possible sites and allocating a set of clients to them in such a way that the maximum distance between a client and the facility to which it is allocated is minimized.…

We study the problem of differentially private clustering under input-stability assumptions. Despite the ever-growing volume of works on differential privacy in general and differentially private clustering in particular, only three works…