1. Robust Local Community Detection: On Free Rider Effect and Its Elimination 1 Case Western Reserve University Yubao Wu 1, Ruoming Jin 2, Jing Li 1, Xiang Zhang 1 2 Kent State University

2. Generic Local Community Detection Problem [1] M. Sozio, et al. KDD’10. [2] W. Cui, et al. SIGMOD’14. [3] L. Ma, et al. DaWak’13. [4] B. Saha, et al. RECOMB’10. [5] C. Tsourakakis, et al. SIGMOD’14. [6] A. Clauset, PRE’05. [7] F. Luo, et al. WIAS’08. [8] R. Andersen, et al. FOCS’06. A

3. Community Goodness Metrics [1] B. Saha, et al. RECOMB’10. [2] C. Tsourakakis, et al. SIGMOD’14. [3] M. Sozio, et al. KDD’10. [4] W. Cui, et al. SIGMOD’14. [5] F. Luo, et al. WIAS’08. [6] K. J. Lang, CIKM’07. [7] R. Andersen, et al. FOCS’06. [8] A. Clauset, PRE’05. IntuitionsGoodness metricsRef. Internal denseness Classic density[1] Edge-surplus[2] Minimum degree[3,4] Internal denseness & external sparseness Subgraph modularity[5] Density-isolation[6] External conductance[7] Boundary sharpness Local modularity[8]

4. Free Rider Effect Goodness metricsA Classic density 2.502.952.83 Edge-surplus 15.326.522.8 Minimum degree 444 Subgraph modularity 2.03.64.6 Density-isolation -2.63.81.5 Ext. conductance 0.250.140.11 Local modularity 0.630.700.78 [1] B. Saha, et al. RECOMB’10. [2] C. Tsourakakis, et al. SIGMOD’14. [3] M. Sozio, et al. KDD’10. [4] W. Cui, et al. SIGMOD’14. [5] F. Luo, et al. WIAS’08. [6] K. J. Lang, CIKM’07. [7] R. Andersen, et al. FOCS’06. [8] A. Clauset, PRE’05.

5. Free Rider Effect in Real Networks (a) Co-author network(b) Biological network Barna, Saha, et al. Dense subgraphs with restrictions and applications to gene annotation graphs. RECOMB, 2010. One existing method: classic density

6. Query Biased Node Weighting Query biased density: Subgraph A becomes the query biased densest subgraph Yubao Wu, Ruoming Jin, Jing Li, and Xiang Zhang. Robust local community detection: on free rider effect and its elimination. PVLDB, 8(7):798-809, 2015.

7. QDC Problem Query biased densest connected subgraph (QDC) problem: Yubao Wu, Ruoming Jin, Jing Li, and Xiang Zhang. Robust local community detection: on free rider effect and its elimination. PVLDB, 8(7):798-809, 2015.

8. QDCQDC’QDC’’ Input ComplexityNP-hardPolynomial QDC Problem and Two Related Problems Optimal Yubao Wu, Ruoming Jin, Jing Li, and Xiang Zhang. Robust local community detection: on free rider effect and its elimination. PVLDB, 8(7):798-809, 2015.

9. Finding the QDC’’ 1. Removing Low Degree Nodes 2. Detect the Densest Subgraph Finding the QDC’ Subgraph contraction Reduce the search space Retain the densest subgraph On the reduced search space Yubao Wu, Ruoming Jin, Jing Li, and Xiang Zhang. Robust local community detection: on free rider effect and its elimination. PVLDB, 8(7):798-809, 2015.

10. Finding the QDC Greedy Node DeletionLocal Expansion 1)Delete low degree nodes 2)Maintain the connectivity 1)Connect the query nodes with a Steiner tree 2)Greedy local expansion Yubao Wu, Ruoming Jin, Jing Li, and Xiang Zhang. Robust local community detection: on free rider effect and its elimination. PVLDB, 8(7):798-809, 2015.

11. Experiments——Datasets Dataset# Nodes# Edges# Communities Amazon00,334,8630,000,925,8720,151,037 DBLP00,317,0800,001,049,8660,013,477 Youtube01,134,8900,002,987,6240,008,385 Orkut03,072,4410,117,185,0836,288,363 LiveJournal03,997,9620,034,681,1890,287,512 Friendster65,608,3661,806,067,1350,957,154 [1] J. Yang and J. Leskovec. Defining and evaluating network communities based on ground-truth. In ICDM, 2012. [2] snap.stanford.edu

12. Experiments——State-of-the-Art Methods ClassesAbbr.Ref.Key Idea Internal denseness DS[1]Densest subgraph with query constraint OQC[2]Optimal quasi-clique; edge-surplus MDG[3]Minimum degree Internal denseness & external sparseness PRN[4]External conductance LS[5]Local spectral EMC[6]More internal edges than external edges SM[7]Subgraph modularity BoundaryLM[8]Local modularity [1] B. Saha, et al. RECOMB’10. [2] C. Tsourakakis, et al. SIGMOD’14. [3] M. Sozio, et al. KDD’10. [4] R. Andersen, et al. FOCS’06. [5] M. W. Mahoney, et al. JMLR’12. [6] G. W. Flake, KDD’00. [7] F. Luo, et al. WIAS’08. [8] A. Clauset, PRE’05.

13. Experiments——Effectiveness Evaluat. Metrics MetricsFormulas F-score Community goodness metrics Density Cohesiveness Separability Consistency [1] J. Yang and J. Leskovec. Dening and evaluating network communities based on ground-truth. In ICDM, pages 745-754, 2012. [2] Ma, Lianhang, et al. GMAC: A seed-insensitive approach to local community detection. In DaWak, pages 297-308, 2013.

14. Effectiveness Evaluation —— F-Score F-scoreQDCDSOQCMDGPRNLSEMCSMLM Amazon0.830.520.540.460.690.660.610.600.58 DBLP0.460.310.330.320.480.420.340.360.37 Youtube0.430.230.220.170.260.240.21 0.22 Orkut0.470.150.160.130.210.170.190.160.18 LiveJournal0.640.480.470.400.520.510.470.480.49 Friendster0.32--0.140.120.170.16--0.140.13 Avg. F-score0.530.30.310.270.390.360.33 Avg. Precision0.650.460.450.290.510.410.340.380.48 Avg. Recall0.780.610.580.690.670.640.660.630.59 Yubao Wu, Ruoming Jin, Jing Li, and Xiang Zhang. Robust local community detection: on free rider effect and its elimination. PVLDB, 8(7):798-809, 2015.

15. Effectiveness Evaluation——Goodness Metrics Community goodness metrics on LiveJournal graph Yubao Wu, Ruoming Jin, Jing Li, and Xiang Zhang. Robust local community detection: on free rider effect and its elimination. PVLDB, 8(7):798-809, 2015.

16. Effectiveness Evaluation——Consistency ConsistencyQDCDSOQCMDGPRNLSEMCSMLM Amazon0.940.770.760.580.790.690.740.670.61 DBLP0.880.620.640.370.650.530.560.430.56 Youtube0.850.610.540.460.710.410.570.370.36 Orkut0.830.560.520.320.680.430.510.540.47 LiveJournal0.930.740.670.430.840.640.730.580.52 Friendster0.78--0.560.450.650.49--0.320.39 Average0.870.640.620.440.720.530.610.49 Yubao Wu, Ruoming Jin, Jing Li, and Xiang Zhang. Robust local community detection: on free rider effect and its elimination. PVLDB, 8(7):798-809, 2015.

17. Conclusions 1) Free rider effect is a serious problem; Yubao Wu, Ruoming Jin, Jing Li, and Xiang Zhang. Robust local community detection: on free rider effect and its elimination. PVLDB, 8(7):798-809, 2015. 2) Query biased node weighting scheme can effectively eliminate the free rider effect thus improve the accuracy.