Advertisement

Rapid Acceleration of the Permutation Test via Transpositions

  • Moo K. ChungEmail author
  • Linhui Xie
  • Shih-Gu Huang
  • Yixian Wang
  • Jingwen Yan
  • Li Shen
Conference paper
  • 663 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11848)

Abstract

The permutation test is an often used test procedure for determining statistical significance in brain network studies. Unfortunately, generating every possible permutation for large-scale brain imaging datasets such as HCP and ADNI with hundreds of subjects is not practical. Many previous attempts at speeding up the permutation test rely on various approximation strategies such as estimating the tail distribution with known parametric distributions. In this study, we propose the novel transposition test that exploits the underlying algebraic structure of the permutation group. The method is applied to a large number of diffusion tensor images in localizing the regions of the brain network differences.

Keywords

Permutation test Transposition test Structural brain networks Permutation group Online statistics computation 

Notes

Acknowledgements

This work was supported by NIH grant R01 EB022856, R01 EB022574 and NSF IIS 1837964. We would like to thank Jean-Baptiste Poline of McGill University, John Kornak of University of California - San Fransisco and Michale A. Newton of University of Wisconsin - Madison for valuable comments and discussions on the mixing time of the transposition test.

References

  1. 1.
    Aldous, D.: Random walks on finite groups and rapidly mixing Markov chains. In: Azéma, J., Yor, M. (eds.) Séminaire de Probabilités XVII 1981/82. LNM, vol. 986, pp. 243–297. Springer, Heidelberg (1983).  https://doi.org/10.1007/BFb0068322CrossRefGoogle Scholar
  2. 2.
    Aldous, D., Diaconis, P.: Shuffling cards and stopping times. Am. Math. Monthly 93, 333–348 (1986)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Avants, B., Epstein, C., Grossman, M., Gee, J.: Symmetric diffeomorphic image registration with cross-correlation: evaluating automated labeling of elderly and neurodegenerative brain. Med. Image Anal. 12, 26–41 (2008)CrossRefGoogle Scholar
  4. 4.
    Avants, B., Tustison, N., Song, G., Cook, P., Klein, A., Gee, J.: A reproducible evaluation of ANTs similarity metric performance in brain image registration. NeuroImage 54, 2033–2044 (2011)CrossRefGoogle Scholar
  5. 5.
    Berestycki, N., Schramm, O., Zeitouni, O.: Mixing times for random k-cycles and coalescence-fragmentation chains. Ann. Probab. 39, 1815–1843 (2011)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Bullmore, E., Suckling, J., Overmeyer, S., Rabe-Hesketh, S., Taylor, E., Brammer, M.: Global, voxel, and cluster tests, by theory and permutation, for difference between two groups of structural MR images of the brain. IEEE Trans. Med. Imaging 18, 32–42 (1999)CrossRefGoogle Scholar
  7. 7.
    Christiaens, D., Reisert, M., Dhollander, T., Sunaert, S., Suetens, P., Maes, F.: Global tractography of multi-shell diffusion-weighted imaging data using a multi-tissue model. NeuroImage 123, 89–101 (2015)CrossRefGoogle Scholar
  8. 8.
    Chung, M.K., Luo, Z., Leow, A.D., Alexander, A.L., Davidson, R.J., Hill Goldsmith, H.: Exact combinatorial inference for brain images. In: Frangi, A.F., Schnabel, J.A., Davatzikos, C., Alberola-López, C., Fichtinger, G. (eds.) MICCAI 2018. LNCS, vol. 11070, pp. 629–637. Springer, Cham (2018).  https://doi.org/10.1007/978-3-030-00928-1_71CrossRefGoogle Scholar
  9. 9.
    Chung, M.K., Villalta-Gil, V., Lee, H., Rathouz, P.J., Lahey, B.B., Zald, D.H.: Exact topological inference for paired brain networks via persistent homology. In: Niethammer, M., et al. (eds.) IPMI 2017. LNCS, vol. 10265, pp. 299–310. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-59050-9_24CrossRefGoogle Scholar
  10. 10.
    Dummit, D., Foote, R.: Abstract Algebra. Wiley, Hoboken (2004)zbMATHGoogle Scholar
  11. 11.
    Embrechts, P., Resnick, S., Samorodnitsky, G.: Extreme value theory as a risk management tool. North Am. Actuarial J. 3, 30–41 (1999)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Feller, W.: An Introduction to Probability Theory and its Applications, vol. 2. Wiley, Hoboken (2008)zbMATHGoogle Scholar
  13. 13.
    Hayasaka, S., Phan, K.L., Liberzon, I., Worsley, K.J., Nichols, T.E.: Nonstationary cluster-size inference with random field and permutation methods. Neuroimage 22, 676–687 (2004)CrossRefGoogle Scholar
  14. 14.
    Hungerford, T.: Algebra. Springer, New York (1980)CrossRefGoogle Scholar
  15. 15.
    Ingalhalikar, M., et al.: Sex differences in the structural connectome of the human brain. Proc. Nat. Acad. Sci. 111, 823–828 (2014)CrossRefGoogle Scholar
  16. 16.
    Jeurissen, B., Tournier, J.D., Dhollander, T., Connelly, A., Sijbers, J.: Multi-tissue constrained spherical deconvolution for improved analysis of multi-shell diffusion MRI data. NeuroImage 103, 411–426 (2014)CrossRefGoogle Scholar
  17. 17.
    Kondor, R., Howard, A., Jebara, T.: Multi-object tracking with representations of the symmetric group. In: International Conference on Artificial Intelligence and Statistics (AISTATS), vol. 1, p. 5 (2007)Google Scholar
  18. 18.
    Lee, H., Kang, H., Chung, M., Lim, S., Kim, B.N., Lee, D.: Integrated multimodal network approach to PET and MRI based on multidimensional persistent homology. Hum. Brain Mapp. 38, 1387–1402 (2017)CrossRefGoogle Scholar
  19. 19.
    Nichols, T., Holmes, A.: Nonparametric permutation tests for functional neuroimaging: a primer with examples. Hum. Brain Mapp. 15, 1–25 (2002)CrossRefGoogle Scholar
  20. 20.
    Smith, R., Tournier, J.D., Calamante, F., Connelly, A.: SIFT2: enabling dense quantitative assessment of brain white matter connectivity using streamlines tractography. NeuroImage 119, 338–351 (2015)CrossRefGoogle Scholar
  21. 21.
    Thompson, P., et al.: Genetic influences on brain structure. Nat. Neurosci. 4, 1253–1258 (2001)CrossRefGoogle Scholar
  22. 22.
    Tournier, J., Calamante, F., Connelly, A., et al.: MRtrix: diffusion tractography in crossing fiber regions. Int. J. Imaging Syst. Technol. 22, 53–66 (2012)CrossRefGoogle Scholar
  23. 23.
    Tzourio-Mazoyer, N., et al.: Automated anatomical labeling of activations in spm using a macroscopic anatomical parcellation of the MNI MRI single-subject brain. NeuroImage 15, 273–289 (2002)CrossRefGoogle Scholar
  24. 24.
    Winkler, A., Ridgway, G., Douaud, G., Nichols, T., Smith, S.: Faster permutation inference in brain imaging. NeuroImage 141, 502–516 (2016)CrossRefGoogle Scholar
  25. 25.
    Worsley, K., Marrett, S., Neelin, P., Vandal, A., Friston, K., Evans, A.: A unified statistical approach for determining significant signals in images of cerebral activation. Hum. Brain Mapp. 4, 58–73 (1996)CrossRefGoogle Scholar
  26. 26.
    Xie, L., et al.: Heritability estimation of reliable connectomic features. In: Wu, G., Rekik, I., Schirmer, M.D., Chung, A.W., Munsell, B. (eds.) CNI 2018. LNCS, vol. 11083, pp. 58–66. Springer, Cham (2018).  https://doi.org/10.1007/978-3-030-00755-3_7CrossRefGoogle Scholar
  27. 27.
    Zalesky, A., et al.: Whole-brain anatomical networks: does the choice of nodes matter? NeuroImage 50, 970–983 (2010)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Moo K. Chung
    • 1
    Email author
  • Linhui Xie
    • 2
  • Shih-Gu Huang
    • 1
  • Yixian Wang
    • 1
  • Jingwen Yan
    • 2
  • Li Shen
    • 3
  1. 1.University of WisconsinMadisonUSA
  2. 2.Indiana University-Purdue University IndianapolisIndianapolisUSA
  3. 3.University of PennsylvaniaPhiladelphiaUSA

Personalised recommendations