Clustering Network Layers with the Strata Multilayer Stochastic Block Model

Stanley, Natalie; Shai, Saray; Taylor, Dane; Mucha, Peter J.

doi:10.1109/tnse.2016.2537545

Cited by 124 publications

(108 citation statements)

References 49 publications

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“…Other studies have further demonstrated that annotated SBMs can be used to constrain community structure based on patterns of neural activity [52], and that SBMs naturally detect higherorder network structures like rich clubs [25]. These applications mirror a more general trend in the network science community where increased emphasis is being placed on developing SBM-related methods for weighted and hierarchical networks [53,54], multi-layer networks [55,56], and annotated graphs [57].…”

Section: Future Work and Extensionsmentioning

confidence: 99%

Non-assortative community structure in resting and task-evoked functional brain networks

Betzel

Bertolero

Bassett

2018

Preprint

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Brain networks exhibit community structure that reconfigures during cognitively demanding tasks. Extant work has emphasized a single class of communities: those that are assortative, or internally dense and externally sparse. Other classes that may play key functional roles in brain function have largely been ignored, leading to an impoverished view in the best case and a mischaracterization in the worst case. Here, we leverage weighted stochastic blockmodeling, a community detection method capable of detecting diverse classes of communities, to study the community structure of functional brain networks while subjects either rest or perform cognitively demanding tasks. We find evidence that the resting brain is largely assortative, although higher order association areas exhibit non-assortative organization, forming cores and peripheries. Surprisingly, this assortative structure breaks down during tasks and is supplanted by core, periphery, and disassortative communities. Using measures derived from the community structure, we show that it is possible to classify an individual's task state with an accuracy that is well above average. Finally, we show that interindividual differences in the composition of assortative and non-assortative communities is correlated with subject performance on in-scanner cognitive tasks. These findings offer a new perspective on the community organization of functional brain networks and its relation to cognition.

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Section: Future Work and Extensionsmentioning

confidence: 99%

Non-assortative community structure in resting and task-evoked functional brain networks

Betzel

Bertolero

Bassett

2018

Preprint

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“…Other methods, such as stochastic blockmodels [63], can detect more general classes of communities. Future work could build on recent applications of blockmodeling to brain network data [64,65] while taking advantage of multi-layer formulations to study multi-subject cohorts [66][67][68]. In addition, the modularity maximization framework is subject to socalled resolution limits [69,70] that, for a given set of parameters, {γ, ω}, render it incapable of resolving communities below some characteristic size.…”

Section: Limitationsmentioning

confidence: 99%

The community structure of functional brain networks exhibits scale-specific patterns of variability across individuals and time

Betzel

Bertolero

Gordon³

et al. 2018

Preprint

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The network organization of the human brain varies across individuals, changes with development and aging, and differs in disease. Discovering the major dimensions along which this variability is displayed remains a central goal of both neuroscience and clinical medicine. Such efforts can be usefully framed within the context of the brain's modular network organization, which can be assessed quantitatively using powerful computational techniques and extended for the purposes of multi-scale analysis, dimensionality reduction, and biomarker generation. Though the concept of modularity and its utility in describing brain network organization is clear, principled methods for comparing multi-scale communities across individuals and time are surprisingly lacking. Here, we present a method that uses multi-layer networks to simultaneously discover the modular structure of many subjects at once. This method builds upon the well-known multi-layer modularity maximization technique, and provides a viable and principled tool for studying differences in network communities across individuals and within individuals across time. We test this method on two datasets and identify consistent patterns of inter-subject community variability, demonstrating that this variability -which would be undetectable using past approaches -is associated with measures of cognitive performance. In general, the multi-layer, multi-subject framework proposed here represents an advancement over current approaches by straighforwardly mapping community assignments across subjects and holds promise for future investigations of inter-subject community variation in clinical populations or as a result of task constraints.

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“…In this case, however, one challenge to face is whether and to what extent an overlapping-aware multilayer modularity should be able to measure the community overlaps within each layer and/or across the layers. Along this direction, it would be interesting to study an integration of our multilayer modularity into recently developed works that propose probabilistic representations or stochastic generative models for overlapping community detection in multilayer networks [49,50].…”

Section: Resultsmentioning

confidence: 99%

Modularity in Multilayer Networks Using Redundancy-Based Resolution and Projection-Based Inter-Layer Coupling

Amelio

Mangioni

Tagarelli

2020

IEEE Trans. Netw. Sci. Eng.

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The generalized version of modularity for multilayer networks, a.k.a. multislice modularity, is characterized by two model parameters, namely resolution factor and inter-layer coupling factor. The former corresponds to a notion of layer-specific relevance, whereas the inter-layer coupling factor represents the strength of node connections across the network layers. Despite the potential of this approach, the setting of both parameters can be arbitrarily selected, without considering specific characteristics from the topology of the multilayer network as well as from an available community structure. Also, the multislice modularity is not designed to explicitly model order relations over the layers, which is of prior importance for dynamic networks.This paper aims to overcome the main limitations of the multislice modularity by introducing a new formulation of modularity for multilayer networks. We revise the role and semantics of both the resolution and inter-layer coupling factors based on information available from the within-layer and inter-layer structures of the multilayer communities. Also, our proposed multilayer modularity is general enough to consider orderings of network layers and their constraints on layer coupling. Experiments were carried out on synthetic and real-world multilayer networks using state-of-the-art approaches for multilayer community detection. The obtained results have shown the meaningfulness of the proposed modularity, revealing the effects of different combinations of the resolution and inter-layer coupling functions. This work also represents a starting point for the development of new optimization methods for community detection in multilayer networks.

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Clustering Network Layers with the Strata Multilayer Stochastic Block Model

Cited by 124 publications

References 49 publications

Non-assortative community structure in resting and task-evoked functional brain networks

Non-assortative community structure in resting and task-evoked functional brain networks

The community structure of functional brain networks exhibits scale-specific patterns of variability across individuals and time

Modularity in Multilayer Networks Using Redundancy-Based Resolution and Projection-Based Inter-Layer Coupling

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