Configuration model for correlation matrices preserving the node strength

Naoki Masuda, Sadamori Kojaku, Yukie Sano

Research output: Contribution to journalArticle (Academic Journal)peer-review

9 Citations (Scopus)
220 Downloads (Pure)

Abstract

Correlation matrices are a major type of multivariate data. To examine properties of a given correlation matrix, a common practice is to compare the same quantity between the original correlation matrix and reference correlation matrices, such as those derived from random matrix theory, that partially preserve properties of the original matrix. We propose a model to generate such reference correlation and covariance matrices for the given matrix. Correlation matrices are often analyzed as networks, which are heterogeneous across nodes in terms of the total connectivity to other nodes for each node. Given this background, the present algorithm generates random networks that preserve the expectation of total connectivity of each node to other nodes, akin to configuration models for conventional networks. Our algorithm is derived from the maximum entropy principle. We will apply the proposed algorithm to measurement of clustering coefficients and community detection, both of which require a null model to assess the statistical significance of the obtained results.

Original languageEnglish
Article number012312
Number of pages18
JournalPhysical Review E
Volume98
Issue number1
Early online date20 Jul 2018
DOIs
Publication statusPublished - Jul 2018

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