A Correlation Clustering Framework for Community Detection

Abstract

Graph clustering, or community detection, is the task of identifying groups of closely related objects in a large network. In this paper we introduce a new community-detection framework called Lamb-daCC that is based on a specially weighted version of correlation clustering. A key component in our methodology is a clustering resolution parameter, λ, which implicitly controls the size and structure of clusters formed by our framework. We show that, by increasing this parameter, our objective effectively interpolates between two different strategies in graph clustering: finding a sparse cut and forming dense subgraphs. Our methodology unifies and generalizes a number of other important clustering quality functions including modularity, sparsest cut, and cluster deletion, and places them all within the context of an optimization problem that has been well studied from the perspective of approximation algorithms. Our approach is particularly relevant in the regime of finding dense clusters, as it leads to a 2-approximation for the cluster deletion problem. We use our approach to cluster several graphs, including large collaboration networks and social networks.

Learning Resolution Parameters for Graph Clustering

“…Our work builds on previous results that introduced generalized objective functions with resolution parameters, including the Hamiltonian objective [30], clustering stability [10], a multiscale variant of the map equation [33], and the LambdaCC framework [38]. Recently Jeub et al [18] introduced a technique for sampling values of a resolution parameter and applying hierarchical consensus clustering techniques.…”

“…As a generalization of standard unweighted correlation clustering, LambdaCC is NPhard, though many approximation algorithms and heuristics for correlation clustering have been developed in practice [2,5,8,9]. In our previous work [38], we showed that a 3approximation for standard LambdaCC can be obtained for any λ ≥ 1/2 by rounding the following LP relaxation of objective (1):…”

“…In this manuscript we focus on a related clustering framework that we developed in previous work [38], based on correlation clustering [5]. This framework is named LambdaCC, after its resolution parameter λ, which implicitly controls both the internal edge density as well as the cut sparsity of nodes formed by minimizing the objective.…”

“…Our Contributions In this paper we develop an approach for learning how to set resolution parameters for both local and global graph clustering problems. Our results for global graph clustering rely heavily on the LambdaCC framework we developed in past work [38]. We begin by formally defining a parameter fitness function for a given clustering.…”

A Parallel Projection Method for Metric Constrained Optimization

“…Metric-constrained optimization problems also frequently arise as convex relaxations of NP-hard graph clustering objectives. A common approach to developing approximation algorithms for these clustering objectives is to first solve a convex relaxation and then round the solution to produce a provably good output clustering [11], [28], [38]. David Gleich is supported by the DARPA Simplex Program, the Sloan Foundation, and NSF awards CCF-1149756, IIS-154648, and CCF-093937.…”