Related papers: A Semidefinite Programming-Based Branch-and-Cut Al…
We introduce a novel method for clustering using a semidefinite programming (SDP) relaxation of the Max k-Cut problem. The approach is based on a new methodology for rounding the solution of an SDP relaxation using iterated linear…
Motivated by applications in community detection and dense subgraph discovery, we consider new clustering objectives in hypergraphs and bipartite graphs. These objectives are parameterized by one or more resolution parameters in order to…
Given a set of data, biclustering aims at finding simultaneous partitions in biclusters of its samples and of the features which are used for representing the samples. Consistent biclusterings allow to obtain correct classifications of the…
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: $+$…
Detecting dense subgraphs from large graphs is a core component in many applications, ranging from social networks mining, bioinformatics. In this paper, we focus on mining dense subgraphs in a bipartite graph. The work is motivated by the…
This paper is related to the problem of finding the maximal quasi-bicliques in a bipartite graph (bigraph). A quasi-biclique in the bigraph is its "almost" complete subgraph. The relaxation of completeness can be understood variously; here,…
Semidefinite programming (SDP) is a powerful tool for tackling a wide range of computationally hard problems such as clustering. Despite the high accuracy, semidefinite programs are often too slow in practice with poor scalability on large…
Fair graph clustering is crucial for ensuring equitable representation and treatment of diverse communities in network analysis. Traditional methods often ignore disparities among social, economic, and demographic groups, perpetuating…
In this paper we study formulations and algorithms for the cycle clustering problem, a partitioning problem over the vertex set of a directed graph with nonnegative arc weights that is used to identify cyclic behavior in simulation data…
This paper proposes a new algorithm for simultaneous graph matching and clustering. For the first time in the literature, these two problems are solved jointly and synergetically without relying on any training data, which brings advantages…
In this article, we continue our analysis for a novel recursive modification to the Max $k$-Cut algorithm using semidefinite programming as its basis, offering an improved performance in vectorized data clustering tasks. Using a dimension…
A linear program with linear complementarity constraints (LPCC) requires the minimization of a linear objective over a set of linear constraints together with additional linear complementarity constraints. This class has emerged as a…
We consider the enumeration of maximal bipartite cliques (bicliques) from a large graph, a task central to many practical data mining problems in social network analysis and bioinformatics. We present novel parallel algorithms for the…
In the biclustering problem, we seek to simultaneously group observations and features. While biclustering has applications in a wide array of domains, ranging from text mining to collaborative filtering, the problem of identifying…
Graph clustering involves the task of dividing nodes into clusters, so that the edge density is higher within clusters as opposed to across clusters. A natural, classic and popular statistical setting for evaluating solutions to this…
The BiCluster Editing problem aims at editing a given bipartite graph into a disjoint union of bicliques via a minimum number of edge deletion or addition operations. As a graph-based model for data clustering, the problem aims at a…
In Bipartite Correlation Clustering (BCC) we are given a complete bipartite graph $G$ with `+' and `-' edges, and we seek a vertex clustering that maximizes the number of agreements: the number of all `+' edges within clusters plus all `-'…
Clustering bipartite graphs is a fundamental task in network analysis. In the high-dimensional regime where the number of rows $n_1$ and the number of columns $n_2$ of the associated adjacency matrix are of different order, existing methods…
We address the problem of un-supervised soft-clustering called micro-clustering. The aim of the problem is to enumerate all groups composed of records strongly related to each other, while standard clustering methods separate records at…
This paper presents the first generic bi-objective binary linear branch-and-cut algorithm. Studying the impact of valid inequalities in solution and objective spaces, two cutting frameworks are proposed. The multi-point separation problem…