Related papers: Universal Algorithms for Clustering Problems
Clustering is a key task in machine learning, with $k$-means being widely used for its simplicity and effectiveness. While 1D clustering is common, existing methods often fail to exploit the structure of 1D data, leading to inefficiencies.…
This paper provides new algorithms for distributed clustering for two popular center-based objectives, k-median and k-means. These algorithms have provable guarantees and improve communication complexity over existing approaches. Following…
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…
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…
We study the design of efficient approximation algorithms for the $\ell$-center clustering and minimum-diameter $\ell$-clustering problems in high dimensional Euclidean and Hamming spaces. Our main tool is randomized dimension reduction.…
Clustering is a well-studied unsupervised learning task that aims to partition data points into a number of clusters. In many applications, these clusters correspond to real-world constructs (e.g., electoral districts, playlists, TV…
Clustering is a widely used and powerful machine learning technique, but its effectiveness is often limited by the need to specify the number of clusters, k, or by relying on thresholds that implicitly determine k. We introduce k*-means, a…
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…
A basic problem in spectral clustering is the following. If a solution obtained from the spectral relaxation is close to an integral solution, is it possible to find this integral solution even though they might be in completely different…
We study the classical metric $k$-median clustering problem over a set of input rankings (i.e., permutations), which has myriad applications, from social-choice theory to web search and databases. A folklore algorithm provides a…
We study a variant of classical clustering formulations in the context of algorithmic fairness, known as diversity-aware clustering. In this variant we are given a collection of facility subsets, and a solution must contain at least a…
Clustering is one of the most fundamental problems in unsupervised learning with a large number of applications. However, classical clustering algorithms assume that the data is static, thus failing to capture many real-world applications…
Clustering is an important task with applications in many fields of computer science. We study the fully dynamic setting in which we want to maintain good clusters efficiently when input points (from a metric space) can be inserted and…
$k$-means clustering is a well-studied problem due to its wide applicability. Unfortunately, there exist strong theoretical limits on the performance of any algorithm for the $k$-means problem on worst-case inputs. To overcome this barrier,…
Capacitated fair-range $k$-clustering generalizes classical $k$-clustering by incorporating both capacity constraints and demographic fairness. In this setting, each facility has a capacity limit and may belong to one or more demographic…
Clustering is a fundamental primitive in unsupervised learning. However, classical algorithms for $k$-clustering (such as $k$-median and $k$-means) assume access to exact pairwise distances -- an unrealistic requirement in many modern…
In metric $k$-clustering, we are given as input a set of $n$ points in a general metric space, and we have to pick $k$ centers and cluster the input points around these chosen centers, so as to minimize an appropriate objective function. In…
We study data clustering problems with $\ell_p$-norm objectives (e.g. $k$-Median and $k$-Means) in the context of individual fairness. The dataset consists of $n$ points, and we want to find $k$ centers such that (a) the objective is…
We study exact recovery conditions for convex relaxations of point cloud clustering problems, focusing on two of the most common optimization problems for unsupervised clustering: $k$-means and $k$-median clustering. Motivations for…
Advances made to the traditional clustering algorithms solves the various problems such as curse of dimensionality and sparsity of data for multiple attributes. The traditional H-K clustering algorithm can solve the randomness and apriority…