Related papers: Partial Optimality in Cubic Correlation Clustering
The higher-order correlation clustering problem for a graph $G$ and costs associated with cliques of $G$ consists in finding a clustering of $G$ so as to minimize the sum of the costs of those cliques whose nodes all belong to the same…
Graph clustering is the problem of identifying sparsely connected dense subgraphs (clusters) in a given graph. Proposed clustering algorithms usually optimize various fitness functions that measure the quality of a cluster within the graph.…
We consider a generalized version of the correlation clustering problem, defined as follows. Given a complete graph $G$ whose edges are labeled with $+$ or $-$, we wish to partition the graph into clusters while trying to avoid errors: $+$…
Several algorithms have been proposed to compute partitions of networks into communities that score high on a graph clustering index called modularity. While publications on these algorithms typically contain experimental evaluations to…
In this paper, we propose and study a semi-random model for the Correlation Clustering problem on arbitrary graphs G. We give two approximation algorithms for Correlation Clustering instances from this model. The first algorithm finds a…
Correlation Clustering is an elegant model that captures fundamental graph cut problems such as Min $s-t$ Cut, Multiway Cut, and Multicut, extensively studied in combinatorial optimization. Here, we are given a graph with edges labeled $+$…
We introduce fast algorithms for correlation clustering with respect to the Min Max objective that provide constant factor approximations on complete graphs. Our algorithms are the first purely combinatorial approximation algorithms for…
Preordering is a generalization of clustering and partial ordering with applications in bioinformatics and social network analysis. Given a finite set $V$ and a value $c_{ab} \in \mathbb{R}$ for every ordered pair $ab$ of elements of $V$,…
Correlation clustering is a technique for aggregating data based on qualitative information about which pairs of objects are labeled 'similar' or 'dissimilar.' Because the optimization problem is NP-hard, much of the previous literature…
In this paper, we present a local information theoretic approach to explicitly learn probabilistic clustering of a discrete random variable. Our formulation yields a convex maximization problem for which it is NP-hard to find the global…
Semi-supervised clustering is a basic problem in various applications. Most existing methods require knowledge of the ideal cluster number, which is often difficult to obtain in practice. Besides, satisfying the must-link constraints is…
Correlation clustering is a central problem in unsupervised learning, with applications spanning community detection, duplicate detection, automated labelling and many more. In the correlation clustering problem one receives as input a set…
In machine learning, correlation clustering is an important problem whose goal is to partition the individuals into groups that correlate with their pairwise similarities as much as possible. In this work, we revisit the correlation…
We describe a new optimization scheme for finding high-quality correlation clusterings in planar graphs that uses weighted perfect matching as a subroutine. Our method provides lower-bounds on the energy of the optimal correlation…
Graph clustering is a fundamental problem that has been extensively studied both in theory and practice. The problem has been defined in several ways in literature and most of them have been proven to be NP-Hard. Due to their high practical…
The question if a given partial solution to a problem can be extended reasonably occurs in many algorithmic approaches for optimization problems. For instance, when enumerating minimal dominating sets of a graph $G=(V,E)$, one usually…
Analysis of higher-order organizations, usually small connected subgraphs called motifs, is a fundamental task on complex networks. This paper studies a new problem of testing higher-order clusterability: given query access to an undirected…
We continue the investigation of problems concerning correlation clustering or clustering with qualitative information, which is a clustering formulation that has been studied recently. The basic setup here is that we are given as input a…
In this paper we study the problem of correlation clustering under fairness constraints. In the classic correlation clustering problem, we are given a complete graph where each edge is labeled positive or negative. The goal is to obtain a…
Motivated by applications in social and biological network analysis, we introduce a new form of agnostic clustering termed~\emph{motif correlation clustering}, which aims to minimize the cost of clustering errors associated with both edges…