Related papers: Multiplicity and Diversity: Analyzing the Optimal …
According to the structural balance theory, a signed graph is considered structurally balanced when it can be partitioned into a number of modules such that positive and negative edges are respectively located inside and between the…
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 $+$…
Correlation clustering provides a method for separating the vertices of a signed graph into the optimum number of clusters without specifying that number in advance. The main goal in this type of clustering is to minimize the number of…
Clustering a signed graph means partitioning the vertices into sets ("clusters") so that every positive edge, and no negative edge, is within a cluster. Clustering is not always possible; the obstruction is circles with exactly one negative…
In signed networks, each edge is labeled as either positive or negative. The edge sign captures the polarity of a relationship. Balance of signed networks is a well-studied property in graph theory. In a balanced (sub)graph, the vertices…
The NP-hard problem of correlation clustering is to partition a signed graph such that the number of conflicts between the partition and the signature of the graph is minimized. This paper studies graph signatures that allow the optimal…
In the correlation clustering problem for complete signed graphs, the input is a complete signed graph with edges weighted as $+1$ (denote recommendation to put this pair in the same cluster) or $-1$ (recommending to put this pair of…
In this work, a graph partitioning problem in a fixed number of connected components is considered. Given an undirected graph with costs on the edges, the problem consists of partitioning the set of nodes into a fixed number of subsets with…
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…
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: $+$…
The clustered planarity problem (c-planarity) asks whether a hierarchically clustered graph admits a planar drawing such that the clusters can be nicely represented by regions. We introduce the cd-tree data structure and give a new…
Correlation clustering is a central topic in unsupervised learning, with many applications in ML and data mining. In correlation clustering, one receives as input a signed graph and the goal is to partition it to minimize the number of…
Correlation Clustering (CC) is a foundational problem in unsupervised learning that models binary similarity relations using labeled graphs. While classical CC has been widely studied, many real-world applications involve more nuanced…
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…
Spectral clustering is sensitive to how graphs are constructed from data particularly when proximal and imbalanced clusters are present. We show that Ratio-Cut (RCut) or normalized cut (NCut) objectives are not tailored to imbalanced data…
We consider inapproximability of the correlation clustering problem defined as follows: Given a graph $G = (V,E)$ where each edge is labeled either "+" (similar) or "-" (dissimilar), correlation clustering seeks to partition the vertices…
As two fundamental problems, graph cuts and graph matching have been investigated over decades, resulting in vast literature in these two topics respectively. However the way of jointly applying and solving graph cuts and matching receives…
Graphs provide an efficient tool for object representation in various computer vision applications. Once graph-based representations are constructed, an important question is how to compare graphs. This problem is often formulated as a…
We study clustering on graphs with multiple edge types. Our main motivation is that similarities between objects can be measured in many different metrics. For instance similarity between two papers can be based on common authors, where…
We propose new mathematical programming models for optimal partitioning of a signed graph into cohesive groups. To demonstrate the approach's utility, we apply it to identify coalitions in US Congress since 1979 and examine the impact of…