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We consider the problem of correlation clustering on graphs with constraints on both the cluster sizes and the positive and negative weights of edges. Our contributions are twofold: First, we introduce the problem of correlation clustering…
Correlation clustering is perhaps the most natural formulation of clustering. Given $n$ objects and a pairwise similarity measure, the goal is to cluster the objects so that, to the best possible extent, similar objects are put in the same…
The emergence of massive graph data sets requires fast mining algorithms. Centrality measures to identify important vertices belong to the most popular analysis methods in graph mining. A measure that is gaining attention is forest…
The wide adoption of Large language models (LLMs) makes their dependability a pressing concern. Detection of errors is the first step to mitigating their impact on a system and thus, efficient error detection for LLMs is an important issue.…
We study LP-rounding approximation algorithms for metric uncapacitated facility-location problems. We first give a new analysis for the algorithm of Chudak and Shmoys, which differs from the analysis of Byrka and Aardal in that now we do…
This paper considers a canonical clustering problem where one receives unlabeled samples drawn from a balanced mixture of two elliptical distributions and aims for a classifier to estimate the labels. Many popular methods including PCA and…
The classic Cluster Editing problem (also known as Correlation Clustering) asks to transform a given graph into a disjoint union of cliques (clusters) by a small number of edge modifications. When applied to vertex-colored graphs (the…
Spectral clustering and its extensions usually consist of two steps: (1) constructing a graph and computing the relaxed solution; (2) discretizing relaxed solutions. Although the former has been extensively investigated, the discretization…
In this work, we provide the first practical evaluation of the structural rounding framework for approximation algorithms. Structural rounding works by first editing to a well-structured class, efficiently solving the edited instance, and…
We consider the {\em clustering with diversity} problem: given a set of colored points in a metric space, partition them into clusters such that each cluster has at least $\ell$ points, all of which have distinct colors. We give a…
We present a method of concatenated quantum error correction in which improved classical processing is used with existing quantum codes and fault-tolerant circuits to more reliably correct errors. Rather than correcting each level of a…
We study the online clustering problem where data items arrive in an online fashion. The algorithm maintains a clustering of data items into similarity classes. Upon arrival of v, the relation between v and previously arrived items is…
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…
Crowdsourced, or human computation based clustering algorithms usually rely on relative distance comparisons, as these are easier to elicit from human workers than absolute distance information. A relative distance comparison is a statement…
Given a finite metric space $(X\cup Y, \mathbf{d})$ the $k$-median problem is to find a set of $k$ centers $C\subseteq Y$ that minimizes $\sum_{p\in X} \min_{c\in C} \mathbf{d}(p,c)$. In general metrics, the best polynomial time algorithm…
Correlation clustering is a well-known unsupervised learning setting that deals with positive and negative pairwise similarities. In this paper, we study the case where the pairwise similarities are not given in advance and must be queried…
Motivated by applications in social network community analysis, we introduce a new clustering paradigm termed motif clustering. Unlike classical clustering, motif clustering aims to minimize the number of clustering errors associated with…
We consider the problem of subspace clustering: given points that lie on or near the union of many low-dimensional linear subspaces, recover the subspaces. To this end, one first identifies sets of points close to the same subspace and uses…
Clustering is a pivotal challenge in unsupervised machine learning and is often investigated through the lens of mixture models. The optimal error rate for recovering cluster labels in Gaussian and sub-Gaussian mixture models involves ad…
Clustering is a basic task in data analysis and machine learning, and the optimization of clustering objectives are well-studied optimization problems; amongst these, the $k$-Means objective is arguably the most well known. Given a…