Related papers: Universal Weak Coreset

Kernel $k$-means clustering is a powerful tool for unsupervised learning of non-linearly separable data. Since the earliest attempts, researchers have noted that such algorithms often become trapped by local minima arising from…

Given a point set $P \subseteq X$ of size $n$ in a metric space $(X,dist)$ of doubling dimension $d$ and two parameters $k \in N$ and $z \in N$, the $k$-center problem with $z$ outliers asks to return a set $C^\ast \subseteq X$ of $k$…

We study core-set construction algorithms for the task of Diversity Maximization under fairness/partition constraint. Given a set of points $P$ in a metric space partitioned into $m$ groups, and given $k_1,\ldots,k_m$, the goal of this…

Coreset selection aims to identify a small yet highly informative subset of data, thereby enabling more efficient model training while reducing storage overhead. Recently, this capability has been leveraged to tackle the challenges of…

Coreset selection targets the challenge of finding a small, representative subset of a large dataset that preserves essential patterns for effective machine learning. Although several surveys have examined data reduction strategies before,…

We study in this paper the problem of maintaining a solution to $k$-median and $k$-means clustering in a fully dynamic setting. To do so, we present an algorithm to efficiently maintain a coreset, a compressed version of the dataset, that…

Centroid based clustering methods such as k-means, k-medoids and k-centers are heavily applied as a go-to tool in exploratory data analysis. In many cases, those methods are used to obtain representative centroids of the data manifold for…

The classical $k$-means algorithm for partitioning $n$ points in $\mathbb{R}^d$ into $k$ clusters is one of the most popular and widely spread clustering methods. The need to respect prescribed lower bounds on the cluster sizes has been…

In this contribution, the clustering procedure based on K-Means algorithm is studied as an inverse problem, which is a special case of the illposed problems. The attempts to improve the quality of the clustering inverse problem drive to…

Many geometric optimization problems can be reduced to finding points in space (centers) minimizing an objective function which continuously depends on the distances from the centers to given input points. Examples are $k$-Means, Geometric…

There is growing empirical evidence that spherical $k$-means clustering performs well at identifying groups of concomitant extremes in high dimensions, thereby leading to sparse models. We provide one of the first theoretical results…

In sensor networks, it is not always practical to set up a fusion center. Therefore, there is need for fully decentralized clustering algorithms. Decentralized clustering algorithms should minimize the amount of data exchanged between…

We study the power of uniform sampling for $k$-Median in various metric spaces. We relate the query complexity for approximating $k$-Median, to a key parameter of the dataset, called the balancedness $\beta \in (0, 1]$ (with $1$ being…

Measuring similarity between two objects is the core operation in existing clustering algorithms in grouping similar objects into clusters. This paper introduces a new similarity measure called point-set kernel which computes the similarity…

Dataset Condensation (DC) aims to obtain a condensed dataset that allows models trained on the condensed dataset to achieve performance comparable to those trained on the full dataset. Recent DC approaches increasingly focus on encoding…

Center-based clustering has attracted significant research interest from both theory and practice. In many practical applications, input data often contain background knowledge that can be used to improve clustering results. In this work,…

$K$-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…

The goal of coreset selection methods is to identify representative subsets of datasets for efficient model training. Yet, existing methods often ignore the possibility of annotation errors and require fixed pruning ratios, making them…

Coreset selection methods have shown promise in reducing the training data size while maintaining model performance for data-efficient machine learning. However, as many datasets suffer from biases that cause models to learn spurious…

We study the problem of constructing $\varepsilon$-coresets for the $(k, z)$-clustering problem in a doubling metric $M(X, d)$. An $\varepsilon$-coreset is a weighted subset $S\subseteq X$ with weight function $w : S \rightarrow…