IEEE ICDE 2016 Black Hole Robust Community Detection

IEEE ICDE 2016 Black. Hole: Robust Community Detection Inspired by Graph Drawing May 17, 2016 Sungsu Lim 1), Junghoon Kim 2), and Jae-Gil Lee 1)* Graduate School of Knowledge Service Engineering, KAIST, Korea 2) LG Electronics, Korea * Corresponding Author 1)

Contents 01. Introduction 02. Proposed Algorithm: Black. Hole 03. Theoretical Validation 04. Performance Evaluation 05. Conclusion 5/17/16 From Interstellar (2014) Black. Hole: Robust Community Detection Inspired by Graph Drawing 2

01 Introduction 5/17/16 Black. Hole: Robust Community Detection Inspired by Graph Drawing 3

Communities in Networks Network Community • A graph representing entities as vertices and their relationships as edges • A set of vertices having similar interests or behaviors / playing similar roles • Internet network Hollywood actor network 3 2 1 Protein-protein interaction network 5/17/16 e. g. , Zachry’s Karate Club 4 Graph representation Black. Hole: Robust Community Detection Inspired by Graph Drawing 4

Community Detection vs. Graph Drawing Community detection • Finding the community structure in a network • Many edges within a community and few edges between communities Graph drawing • Deriving a pictorial representation of a graph • Close positions for adjacent vertices to optimize the aesthetic factor A set of densely-connected vertices gather together A community 5/17/16 Black. Hole: Robust Community Detection Inspired by Graph Drawing 5

Import of Graph Drawing Features Conventional Ours To advance community detection using the features of graph drawing 5/17/16 Black. Hole: Robust Community Detection Inspired by Graph Drawing 6

Key Idea of Our Algorithm Black. Hole l Transformation of community detection to clustering thanks to customized graph drawing Input graph Phase 1: Layout Phase 2: Clustering Community Mapping graph vertices to positions on a lowdimensional space 5/17/16 Detecting clustered regions on the space as communities Black. Hole: Robust Community Detection Inspired by Graph Drawing 7

Main Advantage of Black. Hole l Highly-mixed community structure • Many inter-community edges, in fact, exist among realworld communities • The mixing is defined as the fraction of edges that are between different communities Mixing of each node = 0. 5 Hard to get a clean cut for highly-mixed communities Being robust to highly-mixed communities 5/17/16 Black. Hole: Robust Community Detection Inspired by Graph Drawing 8

02 Proposed Algorithm: Black. Hole 5/17/16 Black. Hole: Robust Community Detection Inspired by Graph Drawing 9

Force-Directed Graph Drawing Strong repulsion between different communities Strong attraction within the same communities 5/17/16 Black. Hole: Robust Community Detection Inspired by Graph Drawing 10

Procedure of Our Graph Drawing (1/2) Randomly, uniformly distribute vertices Iteration Build a quadtree index using the current positions Compute attractive forces between adjacent vertices Compute repulsive forces between every two vertices Determine new positions to reduce the energy Is the energy decreased? No Vertex positions 5/17/16 Yes Phase 2 Black. Hole: Robust Community Detection Inspired by Graph Drawing 11

Procedure of Our Graph Drawing (2/2) l Initial layout: locating vertices randomly l Early iterations: mainly spreading vertices by our design of repulsive forces • The region where positions exist expands rapidly l Later iterations: mainly grouping vertices by our design of attractive forces Initial layout (random) 5/17/16 After 10 iterations After 20 iterations Black. Hole: Robust Community Detection Inspired by Graph Drawing 12

Design of Our Repulsive Forces How to break balls? Increase the force! 5/17/16 Black. Hole: Robust Community Detection Inspired by Graph Drawing 13

Design of Our Attractive Forces Exponential growth in attraction 5/17/16 Black. Hole: Robust Community Detection Inspired by Graph Drawing 14

Phase 1: Layout (1/2) Attraction Repulsion Lin. Log 5/17/16 Black. Hole: Robust Community Detection Inspired by Graph Drawing 15

Phase 1: Layout (2/2) 5/17/16 Whole Region Black. Hole: Robust Community Detection Inspired by Graph Drawing 16

Phase 2: Clustering l Applying conventional clustering algorithms to the vertex positions obtained in Phase I Community Rotation 5/17/16 Black. Hole: Robust Community Detection Inspired by Graph Drawing 17

03 Theoretical Validation 5/17/16 Black. Hole: Robust Community Detection Inspired by Graph Drawing 18

Information Divergence Probability Distribution in Original Space Difference Probability Distribution in Transformed Space 5/17/16 Black. Hole: Robust Community Detection Inspired by Graph Drawing 19

Theoretical Validation (1/2) 5/17/16 Black. Hole: Robust Community Detection Inspired by Graph Drawing 20

Theoretical Validation (2/2) 5/17/16 Black. Hole: Robust Community Detection Inspired by Graph Drawing 21

04 Performance Evaluation 5/17/16 Black. Hole: Robust Community Detection Inspired by Graph Drawing 22

Compared Algorithms l Testing the seven algorithms including ours Algorithm 5/17/16 BH 2 Black. Hole (2 D) BH 3 Black. Hole (3 D) BL Baseline IM Infomap LP Label Propagation LO Louvain SC Spectral Clustering Description Our proposed algorithm Conventional graph drawing + k-means State-of-the-art algorithms Black. Hole: Robust Community Detection Inspired by Graph Drawing 23

Data Sets l Synthetic network: LFR benchmark networks [Lancichinetti and Fortunato 2009] • Varying the mixing, number of vertices, average degree, maximum community size, and so on l Real-world network: # Vertices 5/17/16 # Edges Ave. Degree Clust. Coeff. DBLP 317, 080 1, 049, 866 6. 62 0. 632 Amazon 334, 863 925, 872 5. 53 0. 397 IMDb 1, 324, 748 3, 792, 390 5. 73 0. 000 Youtube 1, 134, 890 2, 987, 624 5. 27 0. 081 Skitter 1, 696, 415 11, 095, 298 13. 08 0. 258 Black. Hole: Robust Community Detection Inspired by Graph Drawing 24

Evaluation Measures l When ground-truth is unknown ← real-world networks • Community-goodness measures [Yang and Leskovec 2012] • A cumulative rank of M 1~M 9 l When ground-truth is known ← synthetic networks • Normalized mutual information (NMI) [Danon et al. 2005] • A measure for comparing different partitioning results, ranging between 0 (disagreement) and 1 (agreement) 5/17/16 Black. Hole: Robust Community Detection Inspired by Graph Drawing 25

Results for Real-World Networks l Two variants of Black. Hole: the best or second best l Spectral: poor because a large number of communities l Baseline: the worst since its layout has weak clustering tendency Cumulative ranks of M 1~M 9 for each algorithm (The lower the rank is, the better an algorithm is) 5/17/16 Black. Hole: Robust Community Detection Inspired by Graph Drawing 26

Results for Synthetic Networks (1/2) Effect of mixing parameter (fraction of inter-community cuts) 5/17/16 Black. Hole: Robust Community Detection Inspired by Graph Drawing 27

Results for Synthetic Networks (2/2) l Robustness to the variation of inter-community cuts • The accuracy of Black. Hole decreases rather slowly (by Corollary 2) l Insensitiveness to the size of a network • The accuracy of most algorithms does not change much Effect of variation of the inter-community cuts 5/17/16 Effect of size of a network Black. Hole: Robust Community Detection Inspired by Graph Drawing 28

Effect of Drawing-Space Dimensionality l Trade-off between performance and accuracy • Accuracy increases to some extent whereas performance decreases exponentially, as the number of dimensions increases • A relatively small number of dimensions, e. g. , 3, is a reasonable choice Effect of dimensionality of the drawing-space 5/17/16 Black. Hole: Robust Community Detection Inspired by Graph Drawing 29

Scalability and Performance of Black. Hole l Near-linear scalability as the network size increases (by Corollary 1) l Performance in between the fastest ones (label propagation, Louvain) and the slowest ones (spectral clustering) Effect of the network size (number of vertices) 5/17/16 Black. Hole: Robust Community Detection Inspired by Graph Drawing 30

05 Conclusion 5/17/16 Black. Hole: Robust Community Detection Inspired by Graph Drawing 31

Conclusions l Proposed a novel paradigm for community detection inspired by graph drawing l Theoretically investigated the relationships between the proposed algorithm and embedding-based algorithms and proved robustness to high mixing l Empirically showed that our algorithm achieves higher accuracy than the state-of-the-art algorithms especially at high mixing 5/17/16 Black. Hole: Robust Community Detection Inspired by Graph Drawing 32

THANK YOU ! 5/17/16 Black. Hole: Robust Community Detection Inspired by Graph Drawing 33