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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
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/BFb0068322
Aldous, D., Diaconis, P.: Shuffling cards and stopping times. Am. Math. Monthly 93, 333–348 (1986)
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)
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)
Berestycki, N., Schramm, O., Zeitouni, O.: Mixing times for random k-cycles and coalescence-fragmentation chains. Ann. Probab. 39, 1815–1843 (2011)
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)
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)
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_71
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_24
Dummit, D., Foote, R.: Abstract Algebra. Wiley, Hoboken (2004)
Embrechts, P., Resnick, S., Samorodnitsky, G.: Extreme value theory as a risk management tool. North Am. Actuarial J. 3, 30–41 (1999)
Feller, W.: An Introduction to Probability Theory and its Applications, vol. 2. Wiley, Hoboken (2008)
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)
Hungerford, T.: Algebra. Springer, New York (1980)
Ingalhalikar, M., et al.: Sex differences in the structural connectome of the human brain. Proc. Nat. Acad. Sci. 111, 823–828 (2014)
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)
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)
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)
Nichols, T., Holmes, A.: Nonparametric permutation tests for functional neuroimaging: a primer with examples. Hum. Brain Mapp. 15, 1–25 (2002)
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)
Thompson, P., et al.: Genetic influences on brain structure. Nat. Neurosci. 4, 1253–1258 (2001)
Tournier, J., Calamante, F., Connelly, A., et al.: MRtrix: diffusion tractography in crossing fiber regions. Int. J. Imaging Syst. Technol. 22, 53–66 (2012)
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)
Winkler, A., Ridgway, G., Douaud, G., Nichols, T., Smith, S.: Faster permutation inference in brain imaging. NeuroImage 141, 502–516 (2016)
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)
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_7
Zalesky, A., et al.: Whole-brain anatomical networks: does the choice of nodes matter? NeuroImage 50, 970–983 (2010)
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.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Chung, M.K., Xie, L., Huang, SG., Wang, Y., Yan, J., Shen, L. (2019). Rapid Acceleration of the Permutation Test via Transpositions. In: Schirmer, M., Venkataraman, A., Rekik, I., Kim, M., Chung, A. (eds) Connectomics in NeuroImaging. CNI 2019. Lecture Notes in Computer Science(), vol 11848. Springer, Cham. https://doi.org/10.1007/978-3-030-32391-2_5
Download citation
DOI: https://doi.org/10.1007/978-3-030-32391-2_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-32390-5
Online ISBN: 978-3-030-32391-2
eBook Packages: Computer ScienceComputer Science (R0)