Related papers: Simple, Scalable and Effective Clustering via One-…
There has been much progress on efficient algorithms for clustering data points generated by a mixture of $k$ probability distributions under the assumption that the means of the distributions are well-separated, i.e., the distance between…
Clustering, a fundamental task in data science and machine learning, groups a set of objects in such a way that objects in the same cluster are closer to each other than to those in other clusters. In this paper, we consider a well-known…
$K$-means, a simple and effective clustering algorithm, is one of the most widely used algorithms in multimedia and computer vision community. Traditional $k$-means is an iterative algorithm---in each iteration new cluster centers are…
Motivated by recent work in computational social choice, we extend the metric distortion framework to clustering problems. Given a set of $n$ agents located in an underlying metric space, our goal is to partition them into $k$ clusters,…
In this paper, we propose a randomly projected convex clustering model for clustering a collection of $n$ high dimensional data points in $\mathbb{R}^d$ with $K$ hidden clusters. Compared to the convex clustering model for clustering…
We initiate the study of the following general clustering problem. We seek to partition a given set $P$ of data points into $k$ clusters by finding a set $X$ of $k$ centers and assigning each data point to one of the centers. The cost of a…
We present a study on how to effectively reduce the dimensions of the $k$-means clustering problem, so that provably accurate approximations are obtained. Four algorithms are presented, two \textit{feature selection} and two \textit{feature…
We revisit the $(f,g)$-clustering problem that we introduced in a recent work [SODA'25], and which subsumes fundamental clustering problems such as $k$-Center, $k$-Median, Min-Sum of Radii, and Min-Load $k$-Clustering. This problem assigns…
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 study the problem of clustering sequences of unlabeled point sets taken from a common metric space. Such scenarios arise naturally in applications where a system or process is observed in distinct time intervals, such as biological…
K-means -- and the celebrated Lloyd algorithm -- is more than the clustering method it was originally designed to be. It has indeed proven pivotal to help increase the speed of many machine learning and data analysis techniques such as…
The invention of the transformer architecture has revolutionized Artificial Intelligence (AI), yielding unprecedented success in areas such as natural language processing, computer vision, and multimodal reasoning. Despite these advances,…
The input to the $k$-median for lines problem is a set $L$ of $n$ lines in $\mathbb{R}^d$, and the goal is to compute a set of $k$ centers (points) in $\mathbb{R}^d$ that minimizes the sum of squared distances over every line in $L$ and its…
Clustering is a NP-hard problem. Thus, no optimal algorithm exists, heuristics are applied to cluster the data. Heuristics can be very resource-intensive, if not applied properly. For substantially large data sets computational efficiencies…
This paper gives a k-means approximation algorithm that is efficient in the relational algorithms model. This is an algorithm that operates directly on a relational database without performing a join to convert it to a matrix whose rows…
The k-means objective is arguably the most widely-used cost function for modeling clustering tasks in a metric space. In practice and historically, k-means is thought of in a continuous setting, namely where the centers can be located…
Finding a good clustering of vertices in a network, where vertices in the same cluster are more tightly connected than those in different clusters, is a useful, important, and well-studied task. Many clustering algorithms scale well,…
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…
Clustering is a separation of data into groups of similar objects. Every group called cluster consists of objects that are similar to one another and dissimilar to objects of other groups. In this paper, the K-Means algorithm is implemented…
Bateni et al. has recently introduced the weak-strong distance oracle model to study clustering problems in settings with limited distance information. Given query access to the strong-oracle and weak-oracle in the weak-strong oracle model,…