IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v109y2017icp76-92.html
   My bibliography  Save this article

Correlation between graphs with an application to brain network analysis

Author

Listed:
  • Fujita, André
  • Takahashi, Daniel Yasumasa
  • Balardin, Joana Bisol
  • Vidal, Maciel Calebe
  • Sato, João Ricardo

Abstract

The global functional brain network (graph) is more suitable for characterizing brain states than local analysis of the connectivity of brain regions. Therefore, graph-theoretic approaches are natural methods to use for studying the brain. However, conventional graph theoretical analyses are limited due to the lack of formal statistical methods of estimation and inference. For example, the concept of correlation between two vectors of graphs has not yet been defined. Thus, the introduction of a notion of correlation between graphs becomes necessary to better understand how brain sub-networks interact. To develop a framework to infer correlation between graphs, one may assume that they are generated by models and that the parameters of the models are the random variables. Then, it is possible to define that two graphs are independent when the random variables representing their parameters are independent. In the real world, however, the model is rarely known, and consequently, the parameters cannot be estimated. By analyzing the graph spectrum, it is shown that the spectral radius is highly associated with the parameters of the graph model. Based on this, a framework for correlation inference between graphs is constructed and the approach illustrated on functional magnetic resonance imaging data on 814 subjects comprising 529 controls and 285 individuals diagnosed with autism spectrum disorder (ASD). Results show that correlations between the default-mode and control, default-mode and somatomotor, and default-mode and visual sub-networks are higher in individuals with ASD than in the controls.

Suggested Citation

  • Fujita, André & Takahashi, Daniel Yasumasa & Balardin, Joana Bisol & Vidal, Maciel Calebe & Sato, João Ricardo, 2017. "Correlation between graphs with an application to brain network analysis," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 76-92.
    • Handle: RePEc:eee:csdana:v:109:y:2017:i:c:p:76-92
    DOI: 10.1016/j.csda.2016.11.016
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947316302900
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2016.11.016?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Fujita, André & Takahashi, Daniel Y. & Patriota, Alexandre G., 2014. "A non-parametric method to estimate the number of clusters," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 27-39.
    2. Borkowf, Craig B., 2002. "Computing the nonnull asymptotic variance and the asymptotic relative efficiency of Spearman's rank correlation," Computational Statistics & Data Analysis, Elsevier, vol. 39(3), pages 271-286, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Fengrong Wei, 2018. "A Short Discussion of Network Analysis," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 7(2), pages 12-13, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Christophe Croux & Catherine Dehon, 2008. "Robustness versus Efficiency for Nonparametric Correlation Measures," Working Papers ECARES 2008_002, ULB -- Universite Libre de Bruxelles.
    2. Christophe Croux & Catherine Dehon, 2010. "Influence functions of the Spearman and Kendall correlation measures," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(4), pages 497-515, November.
    3. Jonas M. B. Haslbeck & Dirk U. Wulff, 2020. "Estimating the number of clusters via a corrected clustering instability," Computational Statistics, Springer, vol. 35(4), pages 1879-1894, December.
    4. Schmid, Friedrich & Schmidt, Rafael, 2007. "Multivariate extensions of Spearman's rho and related statistics," Statistics & Probability Letters, Elsevier, vol. 77(4), pages 407-416, February.
    5. Kojadinovic, Ivan & Yan, Jun, 2010. "Comparison of three semiparametric methods for estimating dependence parameters in copula models," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 52-63, August.
    6. Koltcov, Sergei, 2018. "Application of Rényi and Tsallis entropies to topic modeling optimization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 1192-1204.
    7. Rodel, Egmar & Kossler, Wolfgang, 2004. "Linear rank tests for independence in bivariate distributions--power comparisons by simulation," Computational Statistics & Data Analysis, Elsevier, vol. 46(4), pages 645-660, July.
    8. Perreault, Samuel & Duchesne, Thierry & Nešlehová, Johanna G., 2019. "Detection of block-exchangeable structure in large-scale correlation matrices," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 400-422.
    9. Denis Chetverikov & Daniel Wilhelm, 2023. "Inference for Rank-Rank Regressions," Papers 2310.15512, arXiv.org.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:109:y:2017:i:c:p:76-92. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.