Community detection in temporal multilayer networks, with an application to correlation networks

Bazzi, Marya; Porter, Mason A.; Williams, Stacy; McDonald, Mark W.; Fenn, Daniel J.; Howison, Sam

doi:10.48550/arxiv.1501.00040

Cited by 10 publications

(15 citation statements)

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“…The connection weights in a correlation matrix represent statistical relationships and are not independent of one another; "rewiring" the weights of a correlation matrix can result in a randomized matrix that violates these dependencies and may therefore not be mathematically realizable Zalesky et al (2012). For this reason, several alternative definitions have been proposed for P ij that are appropriate for use with correlation matrices (MacMahon and Garlaschelli, 2013;Bazzi et al, 2014).…”

Section: Single-scale Modularitymentioning

confidence: 99%

Functional brain modules reconfigure at multiple scales across the human lifespan

Betzel,

Mišić,

et al. 2015

Preprint

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The human brain is a complex network of interconnected brain regions organized into functional modules with distinct roles in cognition and behavior. An important question concerns the persistence and stability of these modules over the human lifespan. Here we use graph-theoretic analysis to algorithmically uncover the brain's intrinsic modular organization across multiple spatial scales ranging from small communities comprised of only a few brain regions to large communities made up of many regions. We find that at coarse scales modules become progressively more segregated, while at finer scales segregation decreases. Module composition also exhibits scale-specific and age-dependent changes. At coarse scales, the module assignments of regions normally associated with control, default mode, attention, and visual networks are highly flexible. At fine scales the most flexible regions are associated with the default mode network. Finally, we show that, with age, some regions in the default mode network, specifically retrosplenial cortex, maintain a greater proportion of functional connections to their own module, while regions associated with somatomotor and saliency/ventral attention networks distribute their links more evenly across modules.

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Section: Single-scale Modularitymentioning

confidence: 99%

Functional brain modules reconfigure at multiple scales across the human lifespan

Betzel,

Mišić,

et al. 2015

Preprint

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“…Recently, a variety of techniques have been developed for automatically detecting communities-a task that is similar to traditional clustering [9], but on graphs-in these dynamic networks. These techniques include variants of multilayer or temporal modularity optimization [5,10,11], non-negative matrix or tensor factorization [3,6,8,12,13], minimum description length [14,15], and probabilistic models [4,7,[16][17][18][19][20]. See Refs.…”

mentioning

confidence: 99%

Detectability Thresholds and Optimal Algorithms for Community Structure in Dynamic Networks

et al. 2016

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The detection of communities within a dynamic network is a common means for obtaining a coarsegrained view of a complex system and for investigating its underlying processes. While a number of methods have been proposed in the machine learning and physics literature, we lack a theoretical analysis of their strengths and weaknesses, or of the ultimate limits on when communities can be detected. Here, we study the fundamental limits of detecting community structure in dynamic networks. Specifically, we analyze the limits of detectability for a dynamic stochastic block model where nodes change their community memberships over time, but where edges are generated independently at each time step. Using the cavity method, we derive a precise detectability threshold as a function of the rate of change and the strength of the communities. Below this sharp threshold, we claim that no efficient algorithm can identify the communities better than chance. We then give two algorithms that are optimal in the sense that they succeed all the way down to this threshold. The first uses belief propagation, which gives asymptotically optimal accuracy, and the second is a fast spectral clustering algorithm, based on linearizing the belief propagation equations. These results extend our understanding of the limits of community detection in an important direction, and introduce new mathematical tools for similar extensions to networks with other types of auxiliary information.

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“…We can take different null models for different network types such as directed networks, and bipartite networks, etc. [16], [39]. Traditionally, in an undirected network we take Newman-Girvan null model (i.e.…”

Section: Multilayer Modularity From a Static Perspectivementioning

confidence: 99%

“…In some research a temporal network is defined as a sequence of networks corresponding to successive time points with between-layer couplings indicating the continuity between adjacent layers [14], [39], [42]. For example, suppose in a phone calling temporal network, two nodes are linked by an edge in two successive layers.…”

Section: Temporal Networkmentioning

confidence: 99%

“…In multilayer network analysis, a supra-adjacency always refers to a single-layer network which is flattened from a multilayer network [15], [27], [39], [43], [44]. The basic idea is to combine two layers which are represented by two N × N graphs, to obtain an expanded layer which is represented by a 2 × 2 block graph with the diagonal blocks representing the within-layer adjacency of each layer and off-diagonal blocks representing the between-layer couplings.…”

Section: Supra-adjacency Representation: An Equivalent Single-layer N...mentioning

confidence: 99%

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Modularity in complex multilayer networks with multiple aspects: a static perspective

et al. 2017

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Complex systems are usually illustrated by networks which captures the topology of the interactions between the entities. To better understand the roles played by the entities in the system one needs to uncover the underlying community structure of the system. In recent years, systems with interactions that have various types or can change over time between the entities have attracted an increasing research attention. However, algorithms aiming to solve the key problem -community detection -in multilayer networks are still limited. In this work, we first introduce the multilayer network model representation with multiple aspects, which is flexible to a variety of networks. Then based on this model, we naturally derive the multilayer modularity -a widely adopted objective function of community detection in networks -from a static perspective as an evaluation metric to evaluate the quality of the communities detected in multilayer networks. It enables us to better understand the essence of the modularity by pointing out the specific kind of communities that will lead to a high modularity score. We also propose a spectral method called mSpec for the optimization of the proposed modularity function based on the supra-adjacency representation of the multilayer networks. Experiments on the electroencephalograph network and the comparison results on several empirical multilayer networks demonstrate the feasibility and reliable performance of the proposed method.

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Community detection in temporal multilayer networks, with an application to correlation networks

Cited by 10 publications

References 0 publications

Functional brain modules reconfigure at multiple scales across the human lifespan

Functional brain modules reconfigure at multiple scales across the human lifespan

Detectability Thresholds and Optimal Algorithms for Community Structure in Dynamic Networks

Modularity in complex multilayer networks with multiple aspects: a static perspective

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