RT Journal Article SR Electronic T1 Low rank approximation of difference between correlation matrices by using inner product JF bioRxiv FD Cold Spring Harbor Laboratory SP 2021.02.23.432533 DO 10.1101/2021.02.23.432533 A1 Kensuke Tanioka A1 Satoru Hiwa YR 2021 UL http://biorxiv.org/content/early/2021/02/24/2021.02.23.432533.abstract AB Introduction In the domain of functional magnetic resonance imaging (fMRI) data analysis, given two correlation matrices between regions of interest (ROIs) for the same subject, it is important to reveal relatively large differences to ensure accurate interpretations. However, clustering results based only on difference tend to be unsatisfactory, and interpreting features is difficult because the difference suffers from noise. Therefore, to overcome these problems, we propose a new approach for dimensional reduction clustering.Methods Our proposed dimensional reduction clustering approach consists of low rank approximation and a clustering algorithm. The low rank matrix, which reflects the difference, is estimated from the inner product of the difference matrix, not only the difference. In addition, the low rank matrix is calculated based on the majorize-minimization (MM) algorithm such that the difference is bounded from 1 to 1. For the clustering process, ordinal k-means is applied to the estimated low rank matrix, which emphasizes the clustering structure.Results Numerical simulations show that, compared with other approaches that are based only on difference, the proposed method provides superior performance in recovering the true clustering structure. Moreover, as demonstrated through a real data example of brain activity while performing a working memory task measured by fMRI, the proposed method can visually provide interpretable community structures consisted of well-known brain functional networks which can be associated with human working memory system.Conclusions The proposed dimensional reduction clustering approach is a very useful tool for revealing and interpreting the differences between correlation matrices, even if the true difference tends to be relatively small.Competing Interest StatementThe authors have declared no competing interest.AALautomated anatomical labelingARIadjusted rand indexaCompCoran anatomical component-based noise correction methodBOLDblood oxygen level dependentCONcingulo opercular networkDANdorsal attention networkDMNdefault mode networkEEGelectroencephalographyfMRIfunctional magnetic resonance imagingfNIRSfunctional near-infrared spectroscopyFPNfronto-parietal networkIQRsinterquantile rangesMNIMontreal Neurological InstituteROIsregions of interestSNsalience networkVNvisual networkTPNtask positive networkVANventral attention networkWMWorking Memory.