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Low rank approximation of difference between correlation matrices by using inner product

Kensuke Tanioka, View ORCID ProfileSatoru Hiwa
doi: https://doi.org/10.1101/2021.02.23.432533
Kensuke Tanioka
Department of Biomedical Sciences and Informatics Doshisha University, Kyoto, Japan
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  • For correspondence: ktanioka@mis.doshisha.ac.jp
Satoru Hiwa
Department of Biomedical Sciences and Informatics Doshisha University, Kyoto, Japan
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ABSTRACT

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 Statement

The authors have declared no competing interest.

Footnotes

  • ktanioka{at}mail.doshisha.ac.jp, shiwa{at}mail.doshisha.ac.jp

  • Abbreviations

    AAL
    automated anatomical labeling
    ARI
    adjusted rand index
    aCompCor
    an anatomical component-based noise correction method
    BOLD
    blood oxygen level dependent
    CON
    cingulo opercular network
    DAN
    dorsal attention network
    DMN
    default mode network
    EEG
    electroencephalography
    fMRI
    functional magnetic resonance imaging
    fNIRS
    functional near-infrared spectroscopy
    FPN
    fronto-parietal network
    IQRs
    interquantile ranges
    MNI
    Montreal Neurological Institute
    ROIs
    regions of interest
    SN
    salience network
    VN
    visual network
    TPN
    task positive network
    VAN
    ventral attention network
    WM
    Working Memory.
  • Copyright 
    The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. All rights reserved. No reuse allowed without permission.
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    Posted February 24, 2021.
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    Low rank approximation of difference between correlation matrices by using inner product
    Kensuke Tanioka, Satoru Hiwa
    bioRxiv 2021.02.23.432533; doi: https://doi.org/10.1101/2021.02.23.432533
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    Low rank approximation of difference between correlation matrices by using inner product
    Kensuke Tanioka, Satoru Hiwa
    bioRxiv 2021.02.23.432533; doi: https://doi.org/10.1101/2021.02.23.432533

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