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Hierarchically clustering time-directed graphs and the effects of teleportation and memory Jevin West, Information School, University of Washington Network Clustering Graph Partitioning Community Detection Block Models Module Detection

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Hierarchically clustering time-directed graphs and the effects of teleportation and memory

Jevin West, Information School, University of Washington

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Network Clustering Graph Partitioning Community Detection Block Models Module Detection

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http://www.iloveaba.com/2015/07/no-one-size-does-not-fit-all.html

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No one size fits all

  • No canonical solution or one generalizable

method for all data and all problems (i.e. there is no method that works best on all networks in all situations)

  • Need to know the context for why the user is

interested in clustering

  • We don’t even have a definition of a community
  • Umbrella term for many facets

Schaub, M.T. et al. (2017) The many facets of community detection in complex networks. Applied Network Science

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Cu Cut-bas based: d: community detection as minimization of some form of constraint violation Da Data clus ustering ng: community detection framed as a discretized analogue of data clustering, in which densely knit groups of nodes are to be found Sto Stochas asti tic equival valence: community detection aiming to identify structurally equivalent nodes in a network, leading to notions such as stochastic block models Dy Dyna namics perspective: community detection looking for simplified descriptions of the dynamical flows occurring on the network, that is, some form of dynamical model reduction

No one size fits all

Schaub, M.T. et al. (2017) The many facets of community detection in complex networks. Applied Network Science

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Hierarchical Herd Immunity

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Community Detection Perspectives

Schaub, M.T. et al. (2017) The many facets of community detection in complex networks. Applied Network Science

Circuit layout Minimizing cuts Load balancing Eigenvectors Spectral methods Image segmentation Data Clustering Maximizing node density unknown k, unbalanced Conductance Local, global Modularity Social Networks Connectivity Profiles Stochastic equivalence SBMs, LFR p-values, hypothesis testing Bipartite treatment Predict missing links System behavior, processes Non-adjacency focused Airline network Markovian diffusion process Undirected, Directed InfoMap

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Community Detection Perspectives

Schaub, M.T. et al. (2017) The many facets of community detection in complex networks. Applied Network Science

Circuit layout Minimizing cuts Load balancing Eigenvectors Spectral methods Image segmentation Data Clustering Maximizing node density unknown k, unbalanced Conductance Local, global Modularity Social Networks Connectivity Profiles Stochastic equivalence SBMs, LFR p-values, hypothesis testing Bipartite treatment Predict missing links System behavior, processes Non-adjacency focused Airline network Markovian diffusion process Undirected, Directed InfoMap

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Community Detection Perspectives

Schaub, M.T. et al. (2017) The many facets of community detection in complex networks. Applied Network Science

Circuit layout Minimizing cuts Load balancing Eigenvectors Spectral methods Image segmentation Data Clustering Maximizing node density unknown k, unbalanced Conductance Local, global Modularity Social Networks Connectivity Profiles Stochastic equivalence SBMs, LFR p-values, hypothesis testing Bipartite treatment Predict missing links System behavior, processes Non-adjacency focused Airline network Markovian diffusion process Undirected, Directed InfoMap

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Community Detection Perspectives

Schaub, M.T. et al. (2017) The many facets of community detection in complex networks. Applied Network Science

Circuit layout Minimizing cuts Load balancing Eigenvectors Spectral methods Image segmentation Data Clustering Maximizing node density unknown k, unbalanced Conductance Local, global Modularity Social Networks Connectivity Profiles Stochastic equivalence SBMs, LFR p-values, hypothesis testing Bipartite treatment Predict missing links System behavior, processes Non-adjacency focused Airline network Markovian diffusion process Undirected, Directed InfoMap

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Higher Resolution Maps

Rosvall et al. (2014) Memory in network flows and its effects on spreading dynamics and community

  • detection. Nature Communications
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In the spirit of clustering context…

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The Scholarly Graph

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Tens of millions articles, patents, books Billions of citation links Years: 1600 – 2016 1. Mapping Knowledge Domains 2. Science of Science 3. Hierarchical Navigation 4. Recommendation

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Mapping Knowledge Domains

Rosvall, Martin, and Carl T. Bergstrom. "Multilevel compression of random walks on networks reveals hierarchical organization in large integrated systems." PloS one 6.4 (2011): e18209.

1

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West, J.D. (2012) The Role of Gender in Scholarly Authorship. PLoS One

2

The Role of Gender in Science

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Hierarchical Navigation

3

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West, Wesley-Smith, Bergstrom (2016) A recommendation system based on hierarchical clustering of an article-level citation network. IEEE, Transactions on Big Data (in press)

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Recommendation

Classic Expert

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Community Detection Perspectives

Schaub, M.T. et al. (2017) The many facets of community detection in complex networks. Applied Network Science

Circuit layout Minimizing cuts Load balancing Eigenvectors Spectral methods Image segmentation Data Clustering Maximizing node density unknown k, unbalanced Conductance Local, global Modularity Social Networks Connectivity Profiles Stochastic equivalence SBMs, LFR p-values, hypothesis testing Bipartite treatment Predict missing links System behavior, processes Non-adjacency focused Airline network Markovian diffusion process Undirected, Directed InfoMap

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Finding regularities in citation networks

Rosvall and Bergstrom (2008) PNAS

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Rosvall and Bergstrom (2010) PLoS One

The Emergence of Neuroscience

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Data

Compressing Finding patterns

If we can find a good code for describing flow on a network, we will have solved the dual problem of finding the important structures with respect to that flow.

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frequency of inter-module movements code length of module names frequency of movements within module i code length of node names in module i

The map equation

Rosvall and Bergstrom (2008) PNAS

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Mapequation.org, Daniel Edler

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The relationship between ranking and clustering

Clustering Ranking Dynamics Structure

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Step Length, Teleportation and Memory ..and their effects on ranking and clustering

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Memory: capturing higher order dynamics

Rosvall et al. (2014) Memory in network flows and its effects on spreading dynamics and community

  • detection. Nature Communications
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Memory: capturing higher order dynamics

Rosvall et al. (2014) Memory in network flows and its effects on spreading dynamics and community

  • detection. Nature Communications
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Higher Resolution Maps

Rosvall et al. (2014) Memory in network flows and its effects on spreading dynamics and community

  • detection. Nature Communications
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Higher Order Dynamics

Rosvall et al. (2014) Memory in network flows and its effects on spreading dynamics and community

  • detection. Nature Communications
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Article-level Networks Journal-Level Networks (Memory)

Citation Networks Types

Time-Directed (Acyclic) Graphs

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PageRank Variants (EigenFactor)

P = α H + (1 − α) a.eT

Matrix representing the random walk over citations Probability of not teleporting Cross-citation Matrix dictating the structure

  • f the citation network

Probability of teleporting to completely new journal weighted by the number

  • f articles in that journal

EF =100 Hπ [Hπ]i

i

∑

Leading eigenvector

  • f the random walk

matrix P. Normalization West, JD et al. (2010) College of Research Libraries

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PageRank Pitfalls

Maslov, S. & Redner, S. (2008) Promise and Pitfalls of Extending Google’s PageRank Algorithm to Citation

  • Networks. The Journal of Neuroscience
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teleport DIR-R (PageRank) N O N O D D E E S S ( 1

  • ⍺

) r e c

  • r

d DIR-UR (EigenFactor) don’t record record

  • ther
  • ther
  • ther

in-degree in-out

  • ut-degree

UNDIR:DIR OUTDIR-DIR (Count Links) L I L I N N K K S S d

  • n

’ t r e c

  • r

d

  • u

t

  • d

e g r e e in-out in-degree INDIR:DIR

Teleportation Strategies

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Smart Teleportation

Lambiotte, R. & Rosvall, M. (2012) Ranking and clustering of nodes in networks with smart teleportation

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Smart Teleportation and Clustering

Lambiotte, R. & Rosvall, M. (2012) Ranking and clustering of nodes in networks with smart teleportation

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Article-level Ranking and Mapping

West et al. (2016) Ranking and mapping article-level citation networks. in prep. UNDIR:DIR DIR-R (PageRank) Smooths ranking ~ better clustering

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teleport DIR-R (PageRank) N O N O D D E E S S ( 1 – α ) r e c

  • r

d DIR-UR (EigenFactor) don’t record record

  • ther
  • ther
  • ther

in-degree total

  • ut-degree

UNDIR:DIR OUTDIR-DIR (Count Links) L I L I N N K K S S d

  • n

’ t r e c

  • r

d

  • u

t

  • d

e g r e e total in-degree INDIR:DIR

Teleportation Strategies

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Article-level Eigenfactor

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Running Experiments

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Clustering on time-directed networks

  • Empirical exploration of hierarchical partitions

with varying dynamics

  • The effects of changing recorded teleportation

ranking and clustering

Ranking Effects Clustering Effects

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Article-level Ranking and Mapping

West et al. (2016) Ranking and mapping article-level citation networks. in prep. UNDIR:DIR DIR-R (PageRank) Smooths ranking ~ better clustering

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Revealing Hierarchical Structure

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West, Wesley-Smith, Bergstrom (2016) A recommendation system based on hierarchical clustering of an article-level citation network. IEEE, Transactions on Big Data (in press)

JW JW Recommend

Classic Expert

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Community Detection Perspectives

Schaub, M.T. et al. (2017) The many facets of community detection in complex networks. Applied Network Science

Circuit layout Minimizing cuts Load balancing Eigenvectors Spectral methods Image segmentation Data Clustering Maximizing node density unknown k, unbalanced Conductance Local, global Modularity Social Networks Connectivity Profiles Stochastic equivalence SBMs, LFR p-values, hypothesis testing Bipartite treatment Predict missing links System behavior, processes Non-adjacency focused Airline network Markovian diffusion process Undirected, Directed InfoMap

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Summary

  • Community detection – one size does not fit all
  • Citation networks - dynamical perspective
  • Memory - higher order dynamics
  • Unrecordeded teleportation to links (undirdir)

improves ranking and hierarchical clustering

  • Next steps – building benchmarks and methods

for evaluating the different rankings and hierarchical clusterings (refer to Jennifer Webster’s talk tomorrow)

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Carl Bergstrom, Department of Biology, University of Washington

Acknowledgements

Jason Portenoy, Information School, University of Washington Bill Howe, eScience, CSE, University of Washington Seung-Hee Bae, Computer Science, Western Michigan Martin Rosvall, Department of Physics, Umea University Jennifer Webster, Pacific Northwest National Laboratory

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Jevin West jevinw@uw.edu jevinwest.org @jevinwest