Dynamic Mixed Membership Blockmodel for Evolving Networks

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Dynamic Mixed Membership Blockmodel for Evolving
Networks

• Le Song
• lesong_at_cs.cmu.edu
• Carnegie Mellon University
• Joint work with Wenjie Fu and Eric Xing

6/15/2009
ICML 2009 _at_ Montreal, Canada
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Evolving Networks
Email Networks
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Evolving Networks
Email Networks
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Evolving Networks
Email Networks
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Evolving Networks
Email Networks
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Evolving Networks
Email Networks
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Evolving Networks
Email Networks
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Evolving Networks
Email Networks
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Evolving Networks
Email Networks
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Evolving Networks
Email Networks
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Evolving Networks
Email Networks
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Network Clustering
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Multiple Functionalities
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Multiple Roles
Parent
Teammate
Social Interaction Networks
John
Teacher
Sportsman
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Network Dynamics
Parent
Teammate
Social Interaction Networks
John
John
Teacher
Sportsman
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Network Dynamics
Parent
Teammate
Social Interaction Networks
John
John
Teacher
Sportsman
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Network Dynamics
Parent
Teammate
Social Interaction Networks
John
John
Teacher
Sportsman
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Network Dynamics
Parent
Teammate
Social Interaction Networks
John
John
Teacher
Sportsman
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Network Dynamics
Parent
Teammate
Social Interaction Networks
John
John
Teacher
Sportsman
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Network Dynamics
Parent
Teammate
Social Interaction Networks
John
John
Teacher
Sportsman
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Network Dynamics
Parent
Teammate
Social Interaction Networks
John
John
Teacher
Sportsman
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Dynamic MMSB

• Aim model the evolving mixed membership from
  network sequences
• Experiments Email networks, and gene regulatory
  networks

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Mixed Membership Stochastic Blockmodel
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Mixed Membership Stochastic Blockmodel
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Logistic Normal Prior
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State Space Model
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Dynamic Mixed Membership Blockmodel
State Space Model (SSM) for MMSB Prior
Mixed Membership Stochastic Blockmodel (MMSB)
State Space Model (SSM) for Role Compatibility
Matrix
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• Enron Email Networks
• 151 persons in 2001
• 1 network per month
• 5 latent roles

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Mark Haedicke Managing Director of Legal
Department
Louise Kitchen President of Enron Online
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• Gene Regulatory Networks of Yeast
• 116 genes in 4 epochs
• 1 network per epoch
• 6 latent roles

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Summary

• A visualization and analysis tool for dynamic
  networks
• Incorporate state space model for tracking mixed
  memberships
• Discover interesting pattern from Email networks.

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• Thanks!

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• Synthetic Networks
• Dirichlet vs. Logistic Normal MMSB
• MMSB vs. Dynamic MMSB

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Prediction Error
Role Compatibility Matrix
Tomography
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Learning and Inference for dMMSB

• Variational EM
• Generalized mean field approximation
• Laplace approximation for posterior
• Kalman filter RTS smoother

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Algorithm for dMMSB
Logistic Normal MMSB
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Mixed Membership Stochastic Blockmodel