Clustering of the structures by using “snakes-&-dragons” approach, or correlation matrix as a signal

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.

生物、生态、社会与技术系统均为包含多交互组分的复杂结构，此类系统常以网络（network）形式表征。描述此类系统中变量间相互依赖性的相关矩阵（correlation matrix），可为这类系统的比较与分类提供关键信息。基于相关矩阵的分类方法可补充乃至优化基于变量值的分类方法：前者可揭示系统结构层面的相似性，而后者则依赖系统状态层面的相似性。值得注意的是，此类针对相关矩阵的聚类方法，与针对相关矩阵内部元素的聚类方法截然不同——我们的目标是对多个网络进行比较与聚类，而非网络内部的节点（node）。本文提出一种全新的相关矩阵聚类方法，命名为"snakes-&-dragons"，并通过神经科学、人类微生物组（human microbiome）以及宏观经济学（macroeconomics）领域的实例对该方法进行演示说明。