Abstract
Biological, ecological, social, and technological systems are complex structures with multiple interacting parts, often represented by networks. Correlation matrices describing interdependency of the variables in such structures provide key information for comparison and classification of such systems. Classification based on correlation matrices could supplement or improve classification based on variable values, since the former reveals similarities in system structures, while the latter relies on the similarities in system states. Importantly, this approach of clustering correlation matrices is different from clustering elements of the correlation matrices, because our goal is to compare and cluster multiple networks–not the nodes within the networks. A novel approach for clustering correlation matrices, named “snakes-&-dragons,” is introduced and illustrated by examples from neuroscience, human microbiome, and macroeconomics.
Highlights
Inherent in our human nature is the desire to group similar objects together to better understand the world around us
In clustering brain connectivity matrices from the 37 young and old healthy subjects pilot data set and the GSP data set, we provide the results of clustering and the comparison with existing methods of correlation matrix comparison (RS, T, and S-statistics), and evaluation of the quality of clustering
We presented a novel method named “snakes-&-dragons” for comparing and subtyping of complex systems through clustering of vectors derived from the correlation matrices of the variables describing these systems
Summary
Inherent in our human nature is the desire to group similar objects together to better understand the world around us. It is easy to compare and group objects characterized by a single (scalar) attribute. It becomes more complex when an object is characterized by a vector of multiple attributes, numerous clustering methods already allow for useful classifications of vectors [1]. Some of the most engaging and challenging unresolved questions in biological and social sciences center on the comparison of functions and structures of complex systems. In this case, a system can be characterized by a matrix of interdependencies between its parts and attributes. We aim to extend clustering methods to a task of comparing and classifying objects characterized by correlation matrices
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