Related papers: Coresets for Weight-Constrained Anisotropic Assign…
We suggest efficient and provable methods to compute an approximation for imbalanced point clustering, that is, fitting $k$-centers to a set of points in $\mathbb{R}^d$, for any $d,k\geq 1$. To this end, we utilize \emph{coresets}, which,…
In all state-of-the-art sketching and coreset techniques for clustering, as well as in the best known fixed-parameter tractable approximation algorithms, randomness plays a key role. For the classic $k$-median and $k$-means problems, there…
Clustering under pairwise constraints is an important knowledge discovery tool that enables the learning of appropriate kernels or distance metrics to improve clustering performance. These pairwise constraints, which come in the form of…
We study the effect of Johnson-Lindenstrauss transforms in various projective clustering problems, generalizing recent results which only applied to center-based clustering [MMR19]. We ask the general question: for a Euclidean optimization…
In mixture models, anisotropic noise within each cluster is widely present in real-world data. This work investigates both computationally efficient procedures and fundamental statistical limits for clustering in high-dimensional…
Coresets have emerged as a powerful tool to summarize data by selecting a small subset of the original observations while retaining most of its information. This approach has led to significant computational speedups but the performance of…
Recent work on deep clustering has found new promising methods also for constrained clustering problems. Their typically pairwise constraints often can be used to guide the partitioning of the data. Many problems however, feature…
The coresets approach, also called subsampling or subset selection, aims to select a subsample as a surrogate for the observed sample and has found extensive applications in large-scale data analysis. Existing coresets methods construct the…
In this article, we study shape fitting problems, $\epsilon$-coresets, and total sensitivity. We focus on the $(j,k)$-projective clustering problems, including $k$-median/$k$-means, $k$-line clustering, $j$-subspace approximation, and the…
Clustering methods seek to partition data such that elements are more similar to elements in the same cluster than to elements in different clusters. The main challenge in this task is the lack of a unified definition of a cluster,…
Motivated by the fact that distances between data points in many real-world clustering instances are often based on heuristic measures, Bilu and Linial~\cite{BL} proposed analyzing objective based clustering problems under the assumption…
We construct near-optimal coresets for kernel density estimates for points in $\mathbb{R}^d$ when the kernel is positive definite. Specifically we show a polynomial time construction for a coreset of size $O(\sqrt{d}/\varepsilon\cdot…
We present algorithms that create coresets in an online setting for clustering problems according to a wide subset of Bregman divergences. Notably, our coresets have a small additive error, similar in magnitude to the lightweight coresets…
We present an algorithm for computing $\epsilon$-coresets for $(k, \ell)$-median clustering of polygonal curves in $\mathbb{R}^d$ under the Fr\'echet distance. This type of clustering is an adaption of Euclidean $k$-median clustering: we…
We consider the problem of constructing small coresets for $k$-Median in Euclidean spaces. Given a large set of data points $P\subset \mathbb{R}^d$, a coreset is a much smaller set $S\subset \mathbb{R}^d$, so that the $k$-Median costs of…
Clustering is a fundamental problem, aiming to partition a set of elements, like agents or data points, into clusters such that elements in the same cluster are closer to each other than to those in other clusters. In this paper, we present…
Coreset (or core-set) is a small weighted \emph{subset} $Q$ of an input set $P$ with respect to a given \emph{monotonic} function $f:\mathbb{R}\to\mathbb{R}$ that \emph{provably} approximates its fitting loss $\sum_{p\in P}f(p\cdot x)$ to…
Correlation clustering is a fundamental combinatorial optimization problem arising in many contexts and applications that has been the subject of dozens of papers in the literature. In this problem we are given a general weighted graph…
This paper introduces the equiwide clustering problem, where valid partitions must satisfy intra-cluster dissimilarity constraints. Unlike most existing clustering algorithms, equiwide clustering relies neither on density nor on a…
A limitation of many clustering algorithms is the requirement to tune adjustable parameters for each application or even for each dataset. Some techniques require an \emph{a priori} estimate of the number of clusters while density-based…