Global spectral clustering in dynamic networks

Abstract

Community detection is challenging when the network structure is estimated with uncertainty. Dynamic networks present additional challenges but also add information across time periods. We propose a global community detection method, persistent communities by eigenvector smoothing (PisCES), that combines information across a series of networks, longitudinally, to strengthen the inference for each period. Our method is derived from evolutionary spectral clustering and degree correction methods. Data-driven solutions to the problem of tuning parameter selection are provided. In simulations we find that PisCES performs better than competing methods designed for a low signal-to-noise ratio. Recently obtained gene expression data from rhesus monkey brains provide samples from finely partitioned brain regions over a broad time span including pre- and postnatal periods. Of interest is how gene communities develop over space and time; however, once the data are divided into homogeneous spatial and temporal periods, sample sizes are very small, making inference quite challenging. Applying PisCES to medial prefrontal cortex in monkey rhesus brains from near conception to adulthood reveals dense communities that persist, merge, and diverge over time and others that are loosely organized and short lived, illustrating how dynamic community detection can yield interesting insights into processes such as brain development.

Fast Sequential Clustering in Riemannian Manifolds for Dynamic and Time-Series-Annotated Multilayer Networks

“…The majority of batch-clustering frameworks for multilayer networks has been built on popular learning tools such as subspace learning [37,38], fuzzy clustering [39], the wavelet transform [40], tensor decompositions [41,42], multilayer modularity maximization [16], and graph signal processing [43]. Batch approaches for multilayer networks include also [9,44,45], with [45] being able to address both state clustering and community detection, but not subnetworksequence clustering since inter-layer information cannot be accommodated. Correlation matrices and hierarchical clustering were proposed in [14] to detect communities in multilayer brain networks.…”

Who is really in my social circle?

“…Nevertheless, some community detection algorithms have been applied over temporal networks [35][36][37][38][39][40][41], which represent snapshots as a sequence of static graphs. In this case, the usual approaches detect communities in each snapshot independently [41] or iteratively [40].…”

“…In this case, the usual approaches detect communities in each snapshot independently [41] or iteratively [40]. Other algorithms consider the temporal aspect to identify dynamic communities by globally detecting them in all snapshots [37,38]. Unfortunately, community detection approaches that exploit temporal aspects still comprise a very small part of current work when compared to those based on static networks.…”

A Unified Bayesian Model for Generalized Community Detection in Attribute Networks

“…e detection of communities or modules in a network is conducive to understanding organization rules of complex networks, exploring latent patterns, and predicting the behavior of complex systems. A number of successful community detection approaches have been proposed, which fall into different categories, such as hierarchical clustering algorithms [5,6], modularity optimized approaches [7], statistical inference [8][9][10], spectral algorithms [11][12][13][14], generative model [15][16][17][18], and Markov dynamic algorithms [19][20][21]. For review, the readers can refer to [22].…”