dynamic networks: how networks change with time?

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Dynamic Networks: How Networks Change with Time?. Vahid Mirjalili CSE 891. Overview. Introduction Methodology DHAC : clustering in a single snapshot MATH-EM: Cluster matching in different time frames Results Discussion Further improvement. Motivation. - PowerPoint PPT Presentation

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Dynamic Networks:How Networks Change with Time?Vahid MirjaliliCSE 891

OverviewIntroductionMethodologyDHAC: clustering in a single snapshot MATH-EM: Cluster matching in different time framesResultsDiscussionFurther improvement

MotivationTo infer the dynamic state of a cell in response to physiological changesTwo algorithms used:DHAC: Dynamic Hierarchal Agglomerative Clustering for clustering time-evolving networksMATH-EM: for matching corresponding clusters across time-points

BackgroundCurrent biological networks are staticExperimental methods:Protein abundance (mass spec.) (mainly available for high abundant proteins)Transcript abundance (more readily available)Previous works: combining transcript abundance and interaction networks to create a moving cell

Dynamic NetworksProbabilistic frameworkThe number of proteins can increase or decrease at each time-pointProtein can switch interacting partnersComplexes can grow/shrinkReveals temporal regulation of cell protein state

HAC: Hierarchal Agglomerative ClusteringAgglomerative = bottom up approachDivisive = top down approach

HAC FeaturesMaximizes the likelihood of a hierarchal stochastic block modelAutomatic selection of model sizeMulti-scale networksOutperforms other methods in link prediction

Extending HAC to dynamic networks:

How complexes inferred at one time point correspond to other time pointsTransitions of a protein require dynamic coupling between network snapshots

DHAC:Converting likelihood modularity from maximum likelihood to fully Bayesian statisticsKernelize likelihood modularity with an adaptive bandwidth to couple network clusters at different time pointsDynamic Network Clustering {G(t) = (V(t), E(t)), t= 1 .. T}V: proteins E: (undirected, unweighted) protein-protein interactions

Goal: find the stochastic block models {M(t) t=1 .. T} M(t): network generative model for G(t)

Introducing coupling between time points improves dynamic network clusteringDHAC: notations

probability of a structure model M

The probability that a vertex is in cluster k

Merging ClustersTo merging clusters 1 &2 into 1:

Maximum likelihood

Bayesian

Kernelization

Kernel reweighting: to couple nearby snapshots

DHAC Algorithmfor t=1:T do Set each vertex to be a single cluster Let be cumulative model comparison score Compute merging scores of pairs having an edge or a shared neighbor repeat Pick a pair i,j of maximum Update scores of affected pairs after merging i,j Merge i,j to i' Compute merging scores i',j for all j with or Update until no pairs left output at which was maximumend for

Cluster Matching AlgorithmSearching through time-frames to see how complexes evolveGoal: to find the most probable matching of cluster i to a global index k

ResultsDrosophila development (gene expression data available)

DHAC-local: variable bandwidthDHAC-const: constant bandwidthYeast Metabolic Cycle

Yeast ResultsYeast results identify protein complexes with asynchronous gene expression31 dynamic protein complexes were recoveredMany of the complexes have cluster-specific gene-ontology with P-value