Related papers: Exact Clustering of Weighted Graphs via Semidefini…
Clustering is a well-known and studied problem, one of its variants, called contiguity-constrained clustering, accepts as a second input a graph used to encode prior information about cluster structure by means of contiguity constraints…
We study the problem of recovering a known cluster structure in a sparse network, also known as the planted partitioning problem, by means of statistical mechanics. We find a sharp transition from un-recoverable to recoverable structure as…
The most commonly used method to tackle the graph partitioning problem in practice is the multilevel approach. During a coarsening phase, a multilevel graph partitioning algorithm reduces the graph size by iteratively contracting nodes and…
We study the cluster recovery problem in the semi-supervised active clustering framework. Given a finite set of input points, and an oracle revealing whether any two points lie in the same cluster, our goal is to recover all clusters…
Motivated by a geometric problem, we introduce a new non-convex graph partitioning objective where the optimality criterion is given by the sum of the Dirichlet eigenvalues of the partition components. A relaxed formulation is identified…
Given a collection of vertex-aligned networks and an additional label-shuffled network, we propose procedures for leveraging the signal in the vertex-aligned collection to recover the labels of the shuffled network. We consider matching 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,…
Dense subgraph discovery is an important graph-mining primitive with a variety of real-world applications. One of the most well-studied optimization problems for dense subgraph discovery is the densest subgraph problem, where given an…
Clustering is an effective technique in data mining to generate groups that are the matter of interest. Among various clustering approaches, the family of k-means algorithms and min-cut algorithms gain most popularity due to their…
Mining dense subgraphs is an important primitive across a spectrum of graph-mining tasks. In this work, we formally establish that two recurring characteristics of real-world graphs, namely heavy-tailed degree distributions and large…
Spectral clustering methods which are frequently used in clustering and community detection applications are sensitive to the specific graph constructions particularly when imbalanced clusters are present. We show that ratio cut (RCut) or…
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…
Listing dense subgraphs in large graphs plays a key task in varieties of network analysis applications like community detection. Clique, as the densest model, has been widely investigated. However, in practice, communities rarely form as…
The Cluster Deletion problem takes a graph $G$ as input and asks for a minimum size set of edges $X$ such that $G-X$ is the disjoint union of complete graphs. An equivalent formulation is the Clique Partition problem, which asks to find a…
One of the most useful measures of cluster quality is the modularity of a partition, which measures the difference between the number of the edges joining vertices from the same cluster and the expected number of such edges in a random…
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…
Local clustering aims at extracting a local structure inside a graph without the necessity of knowing the entire graph structure. As the local structure is usually small in size compared to the entire graph, one can think of it as a…
This paper investigates the computational complexity of deciding whether the vertices of a graph can be partitioned into a disjoint union of cliques and a triangle-free subgraph. This problem is known to be $\NP$-complete on arbitrary…
We define a general variant of the graph clustering problem where the criterion of density for the clusters is (high) connectivity. In {\sc Clustering to Given Connectivities}, we are given an $n$-vertex graph $G$, an integer $k$, and a…
Local clustering aims to identify specific substructures within a large graph without any additional structural information of the graph. These substructures are typically small compared to the overall graph, enabling the problem to be…