High-Dimensional Classification for Brain Decoding

Part of the Contributions to Statistics book series (CONTRIB.STAT.)


Brain decoding involves the determination of a subject’s cognitive state or an associated stimulus from functional neuroimaging data measuring brain activity. In this setting the cognitive state is typically characterized by an element of a finite set, and the neuroimaging data comprise voluminous amounts of spatiotemporal data measuring some aspect of the neural signal. The associated statistical problem is one of the classifications from high-dimensional data. We explore the use of functional principal component analysis, mutual information networks, and persistent homology for examining the data through exploratory analysis and for constructing features characterizing the neural signal for brain decoding. We review each approach from this perspective, and we incorporate the features into a classifier based on symmetric multinomial logistic regression with elastic net regularization. The approaches are illustrated in an application where the task is to infer, from brain activity measured with magnetoencephalography (MEG), the type of video stimulus shown to a subject.


Point Cloud Training Sample Simplicial Complex Brain Signal Functional Principal Component Analysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This article is based on work from Nicole Croteau’s MSc thesis. F.S. Nathoo is supported by an NSERC discovery grant and holds a Tier II Canada Research Chair in Biostatistics for Spatial and High-Dimensional Data. The authors thank Rachel Levanger for useful discussions on the implementation of persistent homology for space-time data.


  1. 1.
    Adcock, A., Rubin, D., Carlsson, G.: Classification of hepatic lesions using the matching metric. Comput. Vis. Image Underst. 121, 36–42 (2014)CrossRefGoogle Scholar
  2. 2.
    Bobrowski, O., Kahle, M., Skraba, P.: Maximally persistent cycles in random geometric complexes. arXiv preprint arXiv:1509.04347 (2015)Google Scholar
  3. 3.
    Carlsson, G. Topology and data. Bull. Am. Math. Soc. 46, 255–308 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Chapelle, O., Haffner, P., Vapnik, V.N.: Support vector machines for histogram-based image classification. IEEE Trans. Neural Netw. 10, 1055–1064 (1999)CrossRefGoogle Scholar
  5. 5.
    Chen, D., Müller, H.-G.: Nonlinear manifold representations for functional data. Ann. Stat. 40, 1–29 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Chung, M.K., Bubenik, P., Kim, P.T.: Persistence diagrams of cortical surface data. In: Information Processing in Medical Imaging, pp. 386–397. Springer, Berlin/Heidelberg (2009)Google Scholar
  7. 7.
    Fasy, B.T., Kim, J., Lecci, F., Maria, C.: Introduction to the R package TDA. arXiv preprint arXiv:1411.1830 (2014)Google Scholar
  8. 8.
    Fasy, B.T., Lecci, F., Rinaldo, A., Wasserman, L., Balakrishnan, S., Singh, A.: Confidence sets for persistence diagrams. Ann. Stat. 42 (6), 2301–2339 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Friedman, J., Hastie, T., Tibshirani, R.: Regularization paths for generalized linear models via coordinate descent. J. Stat. Softw. 33, 1–22 (2010)CrossRefGoogle Scholar
  10. 10.
    Friston, K., Chu, C., Mourao-Miranda, J., Hulme, O., Rees, G., Penny, W., Ashburner, J.: Bayesian decoding of brain images. Neuroimage 39, 181–205 (2008)CrossRefGoogle Scholar
  11. 11.
    Haynes, J.-D., Rees, G.: Decoding mental states from brain activity in humans. Nat. Rev. Neurosci. 7, 523–534 (2006)CrossRefGoogle Scholar
  12. 12.
    Heo, G., Gamble, J., Kim, P.T.: Topological analysis of variance and the maxillary complex. J. Am. Stat. Assoc. 107, 477–492 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Huttunen, H., Manninen, T., Kauppi, J.P., Tohka, J.: Mind reading with regularized multinomial logistic regression. Mach. Vis. Appl. 24, 1311–1325 (2013)CrossRefGoogle Scholar
  14. 14.
    Joe, H.: Relative entropy measures of multivariate dependence. J. Am. Stat. Assoc. 84, 157–164 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Klami, A., Ramkumar, P., Virtanen, S., Parkkonen, L., Hari, R., Kaski, S.: ICANN/PASCAL2 challenge: MEG mind reading—overview and results. In: Proceedings of ICANN/PASCAL2 Challenge: MEG Mind Reading (2011)Google Scholar
  16. 16.
    Kramar, M., Levanger, R., Tithof, J., Suri, B., Xu, M., Paul, M., Schatz, M., Mischaikow, K.: Analysis of Kolmogorov flow and Rayleigh-Bénard convection using persistent homology. arXiv preprint arXiv:1505.06168 (2015)Google Scholar
  17. 17.
    Leng, X., Muller, H.G.: Classification using functional data analysis for temporal gene expression data. Bioinformatics 22, 68–76 (2006)CrossRefGoogle Scholar
  18. 18.
    Liu, C., Ray, S., Hooker, G.: Functional principal components analysis of spatially correlated data. arXiv:1411.4681 (2014)Google Scholar
  19. 19.
    Meinshausen, N., Buhlmann, P.: Stability selection. J. R. Stat. Soc. Ser. B 72 (4), 417–473 (2010)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Neal, R.M., Zhang, J.: High dimensional classification with Bayesian neural networks and Dirichlet diffusion trees. In: Feature Extraction. Springer, Berlin/Heidelberg, pp. 265–296 (2006)Google Scholar
  21. 21.
    Pachauri, D., Hinrichs, C., Chung, M.K., Johnson, S.C., Singh, V.: Topology-based kernels with application to inference problems in Alzheimer’s disease. IEEE Trans. Med. Imaging 30, 1760–1770 (2011)CrossRefGoogle Scholar
  22. 22.
    Rasmussen, C.E.: Gaussian processes in machine learning. In: Advanced Lectures on Machine Learning, pp. 63–71. Springer, Berlin/Heidelberg (2004)Google Scholar
  23. 23.
    Ripley, B.D.: Neural networks and related methods for classification. J. R. Stat. Soc. Ser. B Methodol. 56, 409–456 (1994)MathSciNetzbMATHGoogle Scholar
  24. 24.
    Rubinov, M., Sporns, O.: Complex network measures of brain connectivity: uses and interpretations. Neuroimage 52, 1059–1069 (2010)CrossRefGoogle Scholar
  25. 25.
    Sethares, W.A., Budney, R.: Topology of musical data. J. Math. Music 8, 73–92 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Shumway, R.H., Stoffer, D.S.: Spectral analysis and filtering. In: Time Series Analysis and Its Applications. Springer, New York (2011)CrossRefzbMATHGoogle Scholar
  27. 27.
    Silverman, B.W., Ramsay, J.O.: Functional Data Analysis. Springer, New York (2005)zbMATHGoogle Scholar
  28. 28.
    Stam, C.J., Breakspear, M., van Walsum, A.M.V.C., van Dijk, B.W.: Nonlinear synchronization in EEG and whole-head MEG recordings of healthy subjects. Hum. Brain Mapp. 19, 63–78 (2003)CrossRefGoogle Scholar
  29. 29.
    Tomioka, R., Aihara, K., Muller, K.-R.: Logistic regression for single trial EEG classification. Adv. Neural Inf. Process. Syst. 19, 1377–1384 (2007)Google Scholar
  30. 30.
    Zhou, D., Thompson, W.K., Siegle, G.: MATLAB toolbox for functional connectivity. Neuroimage 47, 1590–1607 (2009)CrossRefGoogle Scholar
  31. 31.
    Zhu, X.: Persistent homology: an introduction and a new text representation for natural language processing. In: Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence. AAAI Press, Beijing (2013)Google Scholar
  32. 32.
    Zou, H., Hastie, T.: Regularization and variable selection via the elastic net. J. R. Stat. Soc. Ser. B Stat. Methodol. 67, 301–320 (2005)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of VictoriaVictoriaCanada

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