Relative Validity Criteria for Community Mining Evaluation Reihaneh Rabbany, Mansoreh Takaffoli, Justin Fagnan, Osmar R. Zaϊane and Ricardo J. G. B. Campello Department of Computing Science, University of Alberta, Edmonton, Canada ASONAM 2012 Aug 2012

Motivation Applications in different domains; sociology, criminology Module identification in Biological Networks Clusters in Protein-Protein Interaction Networks Protein complexes and parts of pathways; Clusters in a protein similarity network protein families. (R Guimerà et al., Functional cartography of complex metabolic networks, Nature 433, 2005) Prerequisite of further analysis; Targeted advertising, link prediction, recommendation Social Networks: personalized news feed, easier privacy settings Gmail's "Don't Forget Bob!" and "Got the Wrong Bob?" features (M Roth et al., Suggesting Friends Using the Implicit Social Graph, KDD 2010) Citation network of scholars Paper and collaborator recommendation, Network visualization and Navigation; e.g. CiteULike, Arnet Miner and Microsoft Academic Hyperlinks between web pages - WWW Detecting Group of closely related topics to refined search results (J Chen et al., An Unsupervised Approach to Cluster Web Search Results Based on Word Sense Communities. Web Intelligence 2008) 1

Community Loosely defined as groups of nodes that have relatively more links between themselves than to the rest of the network Nodes that have structural similarity (SCAN, Xu et al. 2007) Nodes that are connected with cliques (CFinder by Palla et al. 2005) Nodes that a random walk is likely to trap within them (MCL by Dongen, Walktrap by Pons and Latapy) Nodes that follow the same leader (TopLeaders, 2010) Nodes that make the graph compress efficiently (Infomap, Infomod, Rosvall and Bergstrom, 2011) Nodes that are separated from the rest by min cut, conductance (flow based methods, e.g. Kernighan-Lin (KL), betweenness of Newman) Nodes that number of links between them is more than chance (Newman's Q modularity, FastModularity, Blondel et al.’s Louvain) 2

Evaluation; overlooked Internal Evaluation Predefined quality/structure for the communities Graph partitioning measures (density, conductance) External Evaluation Agreement between the results and a given known ground-truth A clustering similarity/agreement indexes; Rand Index, Jaccard Benchmarks with ground truth; GN(2002), LFR(2008) The community structure is not known beforehand No ground truth No large data set with known ground truth The synthetic benchmarks disagree with some real network characteristics Karate GN LFR 3

Relative Validity Criteria Validity criteria defined for clustering evaluation; compares different clusterings of a same data set We altered criteria Generalized distance; graph distance measures Generalized mean/centroid notion; averaging v.s. medoid e.g. Variance Ratio Criterion (VRC) Same for: Dunn index, Silhouette Width Criterion (SWC), Alternative Silhouette, PBM, C-Index, Z-Statistics, Point-Biserial (PB) Distance Alternatives: Edge Path (ED), Shortest Path Distance (SPD), Adjacency Relation Distance (ARD), Neighbour Overlap Distance (NOD), Pearson Correlation Distance (PCD), ICloseness Distance (ICD) 4

Correlation with External Index Correlation of relative criteria and external scores on different clusterings of same data set random clusterings that range from very close to very far from ground truth For karate; 5

Correlation with External Index Correlation of relative criteria and external scores on different clusterings of same data set random clusterings that range from very close to very far from ground truth For karate; 5

Ranking of Criteria on Real World Benchmarks Difficulty Analysis Data set statistics Overall Ranking 6

Ranking of Criteria on Synthetic Benchmarks Ranking for well separated communities Data set statistics Overall ranking for very mixed communities 7

Ranking varies Criteria Ranking is affected by: Choice of benchmarks, synthetic generator and its parameters Choice of External agreement Index; ARI, NMI, AMI, Jacard Choice of correlation measure; Pearson & Spearman correlation Choice of clustering randomization Get the ranking in your setting www.cs.ualberta.ca/~rabbanyk/criteriaComparison 8

Future Works Evaluation Issues Community mining specific agreement measure Realistic synthetic benchmarks Extensions of criteria Incorporating attributes; combine clustering and community mining for cases for which we have both attributes and relations Incorporating uncertainty and edges with probability ... 9

End Questions? 10

Alternative Distances Edge Path (ED), Shortest Path Distance (SPD), Adjacency Relation Distance (ARD), Neighbour Overlap Distance (NOD), Pearson Correlation Distance (PCD), ICloseness Distance (ICD) A

Relative criteria Variance Ratio Criterion (VRC) Dunn index, Silhouette Width Criterion (SWC), Alternative Silhouette, PBM, Davies-Bouldin C-Index, Point-Biserial (PB) B