Community detection in Multilayer Networks

Transcript

1. Arash Badie Modiri Community Detection in Multilayer Networks
2. JSAT-14
3. Overview • Temporal networks as multilayer networks • Using monolayer community detection methods • Defining a quality function for multilayer networks • Reducibility and clustering of layers
4. Temporal networks as multilayer networks Kivelä, Mikko, et al. "Multilayer networks." Journal of Complex Networks 2.3 (2014): 203-271.
5. Temporal networks as multilayer networks A multilayer network created from a temporal network can be created by connecting same nodes only if they are in sequence or by just forgetting about time and connecting all instances of the same node. You can also keep information about the arrow of time as directed inter- layer connections but it will make things more complicated. Image from: Mucha, Peter J., et al. "Community structure in time-dependent, multiscale, and multiplex networks." science 328.5980 (2010): 876-878.
6. Using monolayer community detection methods on multilayer networks Loe, Chuan Wen, and Henrik Jeldtoft Jensen. "Comparison of communities detection algorithms for multiplex." Physica A: Statistical Mechanics and its Applications 431 (2015): 29-45.
7. Aggregate network • Aggregate all layers and use plain old monolayer methods. • Different methods of aggregation: Binary or Average • Might result in loosing information (more on that later)
8. Consensus across layers Basicly doing community detection on each layer and trying to find a pattern: • Two nodes are in one cluster if they are on the same cluster on more than k layers. • Two intra-layer communities are member of a inter-layer community if they share at least k nodes on all layers. [itemset]
9. Quality function for community detection on multilayer networks Mucha, Peter J., et al. "Community structure in time- dependent, multiscale, and multiplex networks." science 328.5980 (2010): 876-878.
10. Modularity • Fraction of edges falling within groups minus the number expected at random. • Bigger modularity [hopefully] means stronger communities because it means stronger internal links compared to external links. • Not designed for inter-layer links. Image from: Newman, Mark EJ. "Modularity and community structure in networks."Proceedings of the national academy of sciences 103.23 (2006): 8577-8582
11. Multilayer quality • Incorporates a coupling constant (ω) for inter-layer connections and a resolution constant (γ) for each layer. • Any of the heuristic approaches to optimize modularity on monolayer networks can be used with this quality function on multilayer networks. Where C jsr is 0 or ω if node j is connected to itself on layers s and r. Value of k is is total strength of node i on layer s and m s is sum of all strengths across all nodes on layer s. Also g is is the label of group that node i on layer s belongs to.
12. Multilayer quality • Incorporates a coupling constant (ω) for inter-layer connections and a resolution constant (γ) for each layer. • Any of the heuristic approaches to optimize modularity on monolayer networks can be used with this quality function on multilayer networks.
13. Reducibility and clustering of layers De Domenico, Manlio, et al. "Structural reducibility of multilayer networks." Nature communications 6 (2015).
14. Merging layers How many layers, and in what order, can we merge without losing multilayer (temporal) information?
15. Merging layers How many layers, and in what order, can we merge without losing multilayer (temporal) information?
16. Merging two monoplex networks Simply adding up adjacency matrices for two monoplex networks [with same set of nodes].
17. Multilayer information How much more information we have at hand by working with a multilayer network C compared to aggregating all of them into one giant network A? Or how distinguishable is Multilayer network C compared to aggregate network A?
18. Von Neumann entropy • Defined for a single monolayer graph. • “Entanglement of the statistical ensemble of pure states where each pure state is one of the edges of the graph.” • A graph in pure state (h=0) has only one edge. • Can be seen as shannon entropy for graphs. Where λ i is an eigenvalue of the laplacian matrix of the graph G.
19. Distinguishability For a multilayer network A with M layers, and a reduced multilayer network C with X layers (X ≤ M), distinguishability of C compared to aggregation of all layers of A can be defined in terms of entropy per layer of C and entropy of aggregated network.
20. Clustering of layers Using Jensen-Shannon distance to find closest layers on each step to merge, stop on maximum distinguishability. Note: q(C) may (and will) increase by merging layers. This might be a bit counterintuitive.
21. Project: Temporal network of biomedical jargon
22. Biomedical Articles • 26+ millions of papers from PubMed repository from 1800s to a bit in future. [~10 million had english abstracts] • 500+ hand picked words by a group of biomedical science researchers. • Each layer is a network of co- usage of words in abstracts of articles. • A minimum threshold on mutual information used to construct network.
23. Prior art • 5 year intervals studied • No major multilayer study • Results: ◦ emergence of a common core. ◦ consistent trend of increasing interdisciplinarity ◦ Some perks like emergence of syndrome X related communities.
24. My project: Multilayer community detection and clustering of layers • 66 layers from 1950 onward • Multilayer clustering gives more accurate information about trends • clustering layers can tell about disruptions