A density-based statistical analysis of graph clustering algorithm performance

This is a pre-copyedited, author-produced version of an article accepted for publication in Journal of Complex Networks following peer review. The version of record: Pierre Miasnikof, Alexander Y Shestopaloff, Anthony J Bonner, Yuri Lawryshyn, Panos M Pardalos, A density-based statistical analysis of graph clustering algorithm performance, Journal of Complex Networks, Volume 8, Issue 3, June 2020, cnaa012, https://doi.org/10.1093/comnet/cnaa012 is available online at: https://doi.org/10.1093/comnet/cnaa012© 2020 The authors. Published by Oxford University Press. All rights reserved. We introduce graph clustering quality measures based on comparisons of global, intra- A nd inter-cluster densities, an accompanying statistical significance test and a step-by-step routine for clustering quality assessment. Our work is centred on the idea that well-clustered graphs will display a mean intra-cluster density that is higher than global density and mean inter-cluster density. We do not rely on any generative model for the null model graph. Our measures are shown to meet the axioms of a good clustering quality function. They have an intuitive graph-theoretic interpretation, a formal statistical interpretation and can be tested for significance. Empirical tests also show they are more responsive to graph structure, less likely to breakdown during numerical implementation and less sensitive to uncertainty in connectivity than the commonly used measures

Analysis of Network Clustering Algorithms and Cluster Quality Metrics at Scale

Notions of community quality underlie network clustering. 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. We 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 information recovery metrics. 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. Smart local moving is the best performing algorithm in our study, but discrepancies between cluster evaluation metrics prevent us from declaring it absolutely superior. 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

A taxonomy framework for unsupervised outlier detection techniques for multi-type data sets

The term "outlier" can generally be defined as an observation that is significantly different from the other values in a data set. The outliers may be instances of error or indicate events. The task of outlier detection aims at identifying such outliers in order to improve the analysis of data and further discover interesting and useful knowledge about unusual events within numerous applications domains. In this paper, we report on contemporary unsupervised outlier detection techniques for multiple types of data sets and provide a comprehensive taxonomy framework and two decision trees to select the most suitable technique based on data set. Furthermore, we highlight the advantages, disadvantages and performance issues of each class of outlier detection techniques under this taxonomy framework