Constrained Spectral Clustering for Dynamic Community Detection

There has been great interest in recent years on statistical models for dynamic networks. In this paper, I propose a stochastic block transition model (SBTM) for dynamic networks that is inspired by the well-known stochastic block model (SBM) for static networks and previous dynamic extensions of the SBM. Unlike most existing dynamic network models, it does not make a hidden Markov assumption on the edge-level dynamics, allowing the presence or absence of edges to directly in...

Dynamic heterogeneous networks describe the temporal evolution of interactions among nodes and edges of different types. While there is a rich literature on finding communities in dynamic networks, the application of these methods to dynamic heterogeneous networks can be inappropriate, due to the involvement of different types of nodes and edges and the need to treat them differently. In this paper, we propose a statistical framework for detecting common communities in dynami...

Detecting community structures in social networks has gained considerable attention in recent years. However, lack of prior knowledge about the number of communities, and their overlapping nature have made community detection a challenging problem. Moreover, many of the existing methods only consider static networks, while most of real world networks are dynamic and evolve over time. Hence, finding consistent overlapping communities in dynamic networks without any prior knowl...

In the present paper, we studied a Dynamic Stochastic Block Model (DSBM) under the assumptions that the connection probabilities, as functions of time, are smooth and that at most $s$ nodes can switch their class memberships between two consecutive time points. We estimate the edge probability tensor by a kernel-type procedure and extract the group memberships of the nodes by spectral clustering. The procedure is computationally viable, adaptive to the unknown smoothness of t...

Networks built to model real world phenomena are characeterised by some properties that have attracted the attention of the scientific community: (i) they are organised according to community structure and (ii) their structure evolves with time. Many researchers have worked on methods that can efficiently unveil substructures in complex networks, giving birth to the field of community discovery. A novel and challenging problem started capturing researcher interest recently: t...

Community detection is a fundamental problem in network analysis which is made more challenging by overlaps between communities which often occur in practice. Here we propose a general, flexible, and interpretable generative model for overlapping communities, which can be thought of as a generalization of the degree-corrected stochastic block model. We develop an efficient spectral algorithm for estimating the community memberships, which deals with the overlaps by employing ...

Clustering and community detection with multiple graphs have typically focused on aligned graphs, where there is a mapping between nodes across the graphs (e.g., multi-view, multi-layer, temporal graphs). However, there are numerous application areas with multiple graphs that are only partially aligned, or even unaligned. These graphs are often drawn from the same population, with communities of potentially different sizes that exhibit similar structure. In this paper, we dev...

Networks observed in real world like social networks, collaboration networks etc., exhibit temporal dynamics, i.e. nodes and edges appear and/or disappear over time. In this paper, we propose a generative, latent space based, statistical model for such networks (called dynamic networks). We consider the case where the number of nodes is fixed, but the presence of edges can vary over time. Our model allows the number of communities in the network to be different at different t...

Community finding algorithms for networks have recently been extended to dynamic data. Most of these recent methods aim at exhibiting community partitions from successive graph snapshots and thereafter connecting or smoothing these partitions using clever time-dependent features and sampling techniques. These approaches are nonetheless achieving longitudinal rather than dynamic community detection. We assume that communities are fundamentally defined by the repetition of inte...

Most real-world networks evolve over time. Existing literature proposes models for dynamic networks that are either unlabeled or assumed to have a single membership structure. On the other hand, a new family of Mixed Membership Stochastic Block Models (MMSBM) allows to model static labeled networks under the assumption of mixed-membership clustering. In this work, we propose to extend this later class of models to infer dynamic labeled networks under a mixed membership assump...