Abstract
OverviewNotions of community quality underlie the clustering of networks. While studies surrounding network clustering are increasingly common, a precise understanding of the realtionship between different cluster quality metrics is unknown. In this paper, we examine the relationship between stand-alone cluster quality metrics and information recovery metrics through a rigorous analysis of four widely-used network clustering algorithms—Louvain, Infomap, label propagation, and smart local moving. We consider the stand-alone quality metrics of modularity, conductance, and coverage, and we consider the information recovery metrics of adjusted Rand score, normalized mutual information, and a variant of normalized mutual information used in previous work. Our study includes both synthetic graphs and empirical data sets of sizes varying from 1,000 to 1,000,000 nodes.Cluster Quality MetricsWe find significant differences among the results of the different cluster quality metrics. For example, clustering algorithms can return a value of 0.4 out of 1 on modularity but score 0 out of 1 on information recovery. We find conductance, though imperfect, to be the stand-alone quality metric that best indicates performance on the information recovery metrics. Additionally, our study shows that the variant of normalized mutual information used in previous work cannot be assumed to differ only slightly from traditional normalized mutual information.Network Clustering AlgorithmsSmart local moving is the overall best performing algorithm in our study, but discrepancies between cluster evaluation metrics prevent us from declaring it an absolutely superior algorithm. Interestingly, Louvain performed better than Infomap in nearly all the tests in our study, contradicting the results of previous work in which Infomap was superior to Louvain. We find that although label propagation performs poorly when clusters are less clearly defined, it scales efficiently and accurately to large graphs with well-defined clusters.
Highlights
Clustering is the task of assigning a set of objects to groups so that the objects in the same cluster are more similar to each other than to those in other clusters
We evaluate clustering algorithms and cluster quality metrics on graphs ranging from 1,000 to 1M nodes
Our results show overall disagreement between stand-alone quality metrics and information recovery metrics, with conductance as the best of the stand-alone quality metrics
Summary
Clustering is the task of assigning a set of objects to groups ( called classes or categories) so that the objects in the same cluster are more similar (according to a predefined property) to each other than to those in other clusters. The result of clustering may be a hierarchy or partition with disjoint or overlapping clusters. Cluster attributes such as count (number of clusters), average size, minimum size, maximum size, etc., are often of interest. The embedded clustering is treated as a “gold standard,” and clustering algorithms are judged on their ability to recover the information in the embedded clustering. In such synthetic graphs there is a clear definition of rank: the best clustering algorithm is the one that recovers the most information, and the worst clustering algorithm is the one that recovers the least information
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