Abstract
The past decade has been marked with a proliferation of community detection algorithms that aim to organize nodes (e.g., individuals, brain regions, variables) into modular structures that indicate subgroups, clusters, or communities. Motivated by the emergence of big data across many fields of inquiry, these methodological developments have primarily focused on the detection of communities of nodes from matrices that are very large. However, it remains unknown if the algorithms can reliably detect communities in smaller graph sizes (i.e., 1000 nodes and fewer) which are commonly used in brain research. More importantly, these algorithms have predominantly been tested only on binary or sparse count matrices and it remains unclear the degree to which the algorithms can recover community structure for different types of matrices, such as the often used cross-correlation matrices representing functional connectivity across predefined brain regions. Of the publicly available approaches for weighted graphs that can detect communities in graph sizes of at least 1000, prior research has demonstrated that Newman's spectral approach (i.e., Leading Eigenvalue), Walktrap, Fast Modularity, the Louvain method (i.e., multilevel community method), Label Propagation, and Infomap all recover communities exceptionally well in certain circumstances. The purpose of the present Monte Carlo simulation study is to test these methods across a large number of conditions, including varied graph sizes and types of matrix (sparse count, correlation, and reflected Euclidean distance), to identify which algorithm is optimal for specific types of data matrices. The results indicate that when the data are in the form of sparse count networks (such as those seen in diffusion tensor imaging), Label Propagation and Walktrap surfaced as the most reliable methods for community detection. For dense, weighted networks such as correlation matrices capturing functional connectivity, Walktrap consistently outperformed the other approaches for recovering communities.
Highlights
Network theory has been used to examine the organization of networks across disparate research foci, including the World Wide Web (Latora and Marchiori, 2001), social networks (Zachary, 1977), the power grid (Watts and Strogatz, 1998), brain processes (Bassett and Bullmore, 2006), and food-webs (Dunne et al, 2002)
This is evident in neuroimaging studies where community detection is used on functional connectivity correlation matrices obtained from fMRI data (e.g., Mumford et al, 2010; Rubinov and Sporns, 2010) as well as on matrices generated from diffusion tensor imaging (DTI; e.g., Bassett et al, 2011)
The present paper explores which community detection algorithms perform most reliably on graphs conceived as similarity matrices, such as correlation and the reflected difference measure Euclidean distance, which could feasibly be generated for networks such as brain regions of interest
Summary
Network theory has been used to examine the organization of networks across disparate research foci, including the World Wide Web (Latora and Marchiori, 2001), social networks (Zachary, 1977), the power grid (Watts and Strogatz, 1998), brain processes (Bassett and Bullmore, 2006), and food-webs (Dunne et al, 2002). An unintended consequence of this influx is that investigators use algorithms that work well on one type of data or problem (e.g., count matrices; large graphs) on other types of data (e.g., correlation matrices; smaller graphs) for which they have not been evaluated (Orman and Labatut, 2009) This is evident in neuroimaging studies where community detection is used on functional connectivity correlation matrices obtained from fMRI data (e.g., Mumford et al, 2010; Rubinov and Sporns, 2010) as well as on matrices generated from diffusion tensor imaging (DTI; e.g., Bassett et al, 2011). To assist in selecting the appropriate algorithm given the qualities of the data, the present paper offers formal and independent testing of the most commonly used algorithms across different data formats and numerous plausible conditions that likely will be encounter by neural scientists
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