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An Object Oriented Approach to Multimodal Imaging Data in Neuroscience

  • Andrea Cappozzo
  • Federico FerraccioliEmail author
  • Marco Stefanucci
  • Piercesare Secchi
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 257)

Abstract

We propose a methodological framework for exploring complex multimodal imaging data from a neuroscience study with the aim of identifying a data-driven group structure in the patients sample, possibly connected with the presence/absence of lifetime mental disorder. The functional covariances of fMRI signals are first considered as data objects. Appropriate clustering procedures and low dimensional representations are proposed. For inference, a Frechet estimator of both the covariance operator itself and the average covariance operator is used. A permutation procedure to test the equality of the covariance operators between two groups is also considered. We finally propose a method to incorporate spatial dependencies between different brain regions, merging the information from both the Structural Networks and the Dynamic functional activity.

Keywords

Data objects Functional data analysis Principal components Multimodal Imaging Neuroscience 

Notes

Acknowledgements

We acknowledge Greg Kiar and Eric Bridgeford from NeuroData at Johns Hopkins University, who pre-processed the raw DTI and R-fMRI imaging data available at http://fcon_1000.projects.nitrc.org/indi/CoRR/html/nki_1.html. We would like to deeply thank the StartUp Research Scientific Committee for efficiently and flawlessly organizing such a motivating experience. We thank Professor Francesca Greselin and Doctor Mauro Ceroni for their support and help throughout the drafting of this manuscript.

References

  1. 1.
    Amari, S.I.: Differential-geometrical methods in statistics. Lecture Notes in Statistics, vol. 28. Springer, New York (1985)CrossRefGoogle Scholar
  2. 2.
    Bosq, D.: Linear Processes in Function Spaces. Lecture Notes in Statistics. Springer, New York (2000)CrossRefGoogle Scholar
  3. 3.
    Canale, A., Durante, D., Paci, L., Scarpa, B.: Connecting statistical brains. Significance 15(1), 38–40 (2018)CrossRefGoogle Scholar
  4. 4.
    Cole, D.M., Smith, S.M., Beckmann, C.F.: Advances and pitfalls in the analysis and interpretation of resting-state FMRI data. Front. Syst. Neurosci. 4, 8 (2010)Google Scholar
  5. 5.
    Desikan, R.S., Ségonne, F., Fischl, B., Quinn, B.T., Dickerson, B.C., Blacker, D., Buckner, R.L., Dale, A.M., Maguire, R.P., Hyman, B.T., Albert, M.S., Killiany, R.J.: An automated labeling system for subdividing the human cerebral cortex on MRI scans into gyral based regions of interest. NeuroImage 31(3), 968–980 (2006)CrossRefGoogle Scholar
  6. 6.
    Dryden, I.L., Koloydenko, A., Zhou, D.: Non-Euclidean statistics for covariance matrices, with applications to diffusion tensor imaging. Ann. Appl. Stat. 3(3), 1102–1123 (2009)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Friendly, M., Monette, G., Fox, J.: Elliptical insights: understanding statistical methods through elliptical geometry. Stat. Sci. 28(1), 1–39 (2013)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Heuvel, M.P.V.D., Pol, H.E.H.: Exploring the brain network: a review on resting-state fMRI functional connectivity. Eur. Neuropsychopharmacol. 20(8), 519–534 (2010)CrossRefGoogle Scholar
  9. 9.
    Horváth, L., Kokoszka, P.: Inference for Functional Data with Applications. Springer Series in Statistics. Springer, New York (2012)CrossRefGoogle Scholar
  10. 10.
    Hsing, T., Eubank, R.: Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators. Wiley Series in Probability and Statistics. Wiley, Chichester, UK (2015)Google Scholar
  11. 11.
    Huckemann, S.: Intrinsic inference on the mean geodesic of planar shapes and tree discrimination by leaf growth. Ann. Stat. 39(2), 1098–1124 (2010)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Jolliffe, I.T.: Principal Component Analysis and Factor Analysis, pp. 115–128. Springer, New York (1986)CrossRefGoogle Scholar
  13. 13.
    Mallat, S.: A Wavelet Tour of Signal Processing. Academic Press (1999)Google Scholar
  14. 14.
    Marron, J.S., Alonso, A.M.: Overview of object oriented data analysis. Biom. J. 56(5), 732–753 (2014)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Murtagh, F., Legendre, P.: Ward’s hierarchical clustering method: clustering criterion and agglomerative algorithm. J. Classif. 31(3), 274–295 (2011)CrossRefGoogle Scholar
  16. 16.
    Pesarin, F., Salmaso, L.: Permutation Tests for Complex Data: Theory, Applications and Software. Wiley (2010)Google Scholar
  17. 17.
    Pigoli, D., Aston, J.A.D., Dryden, I.L., Secchi, P.: Distances and inference for covariance operators. Biometrika 101(2), 409–422 (2014)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Plis, S., Meinecke, F.C., Eichele, T.: Analysis of multimodal neuroimaging data. IEEE Rev. Biomed. Eng. 4, 26–58 (2011)CrossRefGoogle Scholar
  19. 19.
    Ramsay, J., Silverman, B.W.: Functional Data Analysis. Springer Series in Statistics. Springer, New York (2005)Google Scholar
  20. 20.
    Roalf, D., Gur, R.: Functional brain imaging in neuropsychology over the past 25 years. Neuropsychology 31(8), 954–971 (2017)CrossRefGoogle Scholar
  21. 21.
    Roweis, S.T., Saul, L.K.: Nonlinear dimensionality reduction by locally linear embedding. Science 290(5500), 2323–2326 (2000)CrossRefGoogle Scholar
  22. 22.
    Schur, J.: Bemerkungen zur Theorie der beschränkten Bilinearformen mit unendlich vielen Veränderlichen. J. Reine Angew. Math. 140, 1–28 (1911)MathSciNetzbMATHGoogle Scholar
  23. 23.
    Secchi, P., Vantini, S., Zanini, P.: Hierarchical independent component analysis: a multi-resolution non-orthogonal data-driven basis. Comput. Stat. Data Anal. 95, 133–149 (2016)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Wang, H., Marron, J.S.: Object oriented data analysis: sets of trees. Ann. Stat. 35(5), 1849–1873 (2007)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Andrea Cappozzo
    • 1
  • Federico Ferraccioli
    • 2
    Email author
  • Marco Stefanucci
    • 3
  • Piercesare Secchi
    • 4
  1. 1.Department of Statistics and Quantitative MethodsUniversity of Milano-BicoccaMilanItaly
  2. 2.Department of Statistical SciencesUniversity of PadovaPaduaItaly
  3. 3.Department of Statistical SciencesSapienza University of RomeRomeItaly
  4. 4.MOX Department of MathematicsPolitecnico di MilanoMilanItaly

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