Link-Prediction Enhanced Consensus Clustering for Complex Networks

Many real networks that are inferred or collected from data are incomplete due to missing edges. Missing edges can be inherent to the dataset (Facebook friend links will never be complete) or the result of sampling (one may only have access to a portion of the data). The consequence is that downstream analyses that consume the network will often yield less accurate results than if the edges were complete. Community detection algorithms, in particular, often suffer when critical intra-community edges are missing. We propose a novel consensus clustering algorithm to enhance community detection on incomplete networks. Our framework utilizes existing community detection algorithms that process networks imputed by our link prediction based algorithm. The framework then merges their multiple outputs into a final consensus output. On average our method boosts performance of existing algorithms by 7% on artificial data and 17% on ego networks collected from Facebook

Bayesian stochastic blockmodeling

This chapter provides a self-contained introduction to the use of Bayesian inference to extract large-scale modular structures from network data, based on the stochastic blockmodel (SBM), as well as its degree-corrected and overlapping generalizations. We focus on nonparametric formulations that allow their inference in a manner that prevents overfitting, and enables model selection. We discuss aspects of the choice of priors, in particular how to avoid underfitting via increased Bayesian hierarchies, and we contrast the task of sampling network partitions from the posterior distribution with finding the single point estimate that maximizes it, while describing efficient algorithms to perform either one. We also show how inferring the SBM can be used to predict missing and spurious links, and shed light on the fundamental limitations of the detectability of modular structures in networks.Comment: 44 pages, 16 figures. Code is freely available as part of graph-tool at https://graph-tool.skewed.de . See also the HOWTO at https://graph-tool.skewed.de/static/doc/demos/inference/inference.htm

Element-centric clustering comparison unifies overlaps and hierarchy

Clustering is one of the most universal approaches for understanding complex data. A pivotal aspect of clustering analysis is quantitatively comparing clusterings; clustering comparison is the basis for many tasks such as clustering evaluation, consensus clustering, and tracking the temporal evolution of clusters. In particular, the extrinsic evaluation of clustering methods requires comparing the uncovered clusterings to planted clusterings or known metadata. Yet, as we demonstrate, existing clustering comparison measures have critical biases which undermine their usefulness, and no measure accommodates both overlapping and hierarchical clusterings. Here we unify the comparison of disjoint, overlapping, and hierarchically structured clusterings by proposing a new element-centric framework: elements are compared based on the relationships induced by the cluster structure, as opposed to the traditional cluster-centric philosophy. We demonstrate that, in contrast to standard clustering similarity measures, our framework does not suffer from critical biases and naturally provides unique insights into how the clusterings differ. We illustrate the strengths of our framework by revealing new insights into the organization of clusters in two applications: the improved classification of schizophrenia based on the overlapping and hierarchical community structure of fMRI brain networks, and the disentanglement of various social homophily factors in Facebook social networks. The universality of clustering suggests far-reaching impact of our framework throughout all areas of science

A Method Based on Total Variation for Network Modularity Optimization using the MBO Scheme

The study of network structure is pervasive in sociology, biology, computer science, and many other disciplines. One of the most important areas of network science is the algorithmic detection of cohesive groups of nodes called "communities". One popular approach to find communities is to maximize a quality function known as {\em modularity} to achieve some sort of optimal clustering of nodes. In this paper, we interpret the modularity function from a novel perspective: we reformulate modularity optimization as a minimization problem of an energy functional that consists of a total variation term and an $\ell_2$ balance term. By employing numerical techniques from image processing and $\ell_1$ compressive sensing -- such as convex splitting and the Merriman-Bence-Osher (MBO) scheme -- we develop a variational algorithm for the minimization problem. We present our computational results using both synthetic benchmark networks and real data.Comment: 23 page