Using Algorithmic Complexity to Differentiate Cognitive States in fMRI

  • Mario VentrescaEmail author
Conference paper
Part of the Studies in Computational Intelligence book series (SCI, volume 813)


Functional magnetic resonance imaging data has been increasingly available in recent years, and will continue to increase in volume for the foreseeable future. The ability to model this data as a complex network, and to analyze the resulting networks for patterns that reveal insight into the structure-function relationship of the brain has been a significant development. Despite the progress made, there remains a number of important open questions where a network science perspective may prove insightful. In this paper we perform an empirical investigation into whether the Kolmogorov complexity of the adjacency matrix of a functional brain network can be used to discern what cognitive task a subject is performing, or whether they are in a resting state. The complexity is approximated using the Block Decomposition Method (BMD), and our analysis also provides comparison to the block entropy and compression length (by gzip). Subject data was acquired from the Human Connectome Project, Release Q3. This initial investigation finds that BDM is capable of discerning resting state from other tasks, and provides hints that further development of the method for brain networks if using larger block sizes may be capable of further distinguishing between tasks.


Algorithmic complexity Block decomposition method Brain network 



Data were provided [in part] by the Human Connectome Project, WU-Minn Consortium (Principal Investigators: David Van Essen and Kamil Ugurbil; 1U54MH091657) funded by the 16 NIH Institutes and Centers that support the NIH Blueprint for Neuroscience Research; and by the McDonnell Center for Systems Neuroscience at Washington University. The author would also like to thank Enrico Amico, Joaquin Goñi and Dali Guo for valuable discussions and data processing.


  1. 1.
    Amico, E., Goñi, J.: Maximizing the individual fingerprints of human functional connectomes through decomposition into brain connectivity modes (2017). arXiv preprint arXiv:1707.02365
  2. 2.
    Amico, E., Goñi, J.: The quest for identifiability in human functional connectomes. Sci. Rep. 8(1), 8254 (2018)CrossRefGoogle Scholar
  3. 3.
    Bassett, D.S., Zurn, P., Gold, J.I.: On the nature and use of models in network neuroscience. Nat. Rev. Neurosci. 1 (2018)Google Scholar
  4. 4.
    Betzel, R.F., Bassett, D.S.: Generative models for network neuroscience: prospects and promise. J. R. Soc. Interface 14(136), 20170623 (2017).
  5. 5.
    Bonmati, E., Bardera, A., Feixas, M., Boada, I.: Novel brain complexity measures based on information theory. Entropy 20(7), 491 (2018)CrossRefGoogle Scholar
  6. 6.
    Campani, C.A., Menezes, P.B.: On the application of kolmogorov complexity to the characterization and evaluation of computational models and complex systems. In: Conference on Imaging Science, Systems and Technology, pp. 63–68 (2004)Google Scholar
  7. 7.
    Carhart-Harris, R.L., et al.: The entropic brain: a theory of conscious states informed by neuroimaging research with psychedelic drugs. Front. Hum. Neurosci. 8, 20 (2014)CrossRefGoogle Scholar
  8. 8.
    Casali, A.G., et al.: A theoretically based index of consciousness independent of sensory processing and behavior. Sci. Transl. Med. 5(198), 198ra105–198ra105 (2013)Google Scholar
  9. 9.
    Chaitin, G.J.: On the length of programs for computing finite binary sequences: statistical considerations. J. ACM 16(1), 145–159 (1969)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Delahaye, J.P., Zenil, H.: Numerical evaluation of algorithmic complexity for short strings: a glance into the innermost structure of randomness. Appl. Math. Comput. 219(1), 63–77 (2012)zbMATHGoogle Scholar
  11. 11.
    Fornito, A., Zalesky, A., Breakspear, M.: Graph analysis of the human connectome: promise, progress, and pitfalls. Neuroimage 80, 426–444 (2013)CrossRefGoogle Scholar
  12. 12.
    Gauvrit, N., Zenil, H., Soler-Toscano, F., Delahaye, J.P., Brugger, P.: Human behavioral complexity peaks at age 25. PLoS Comput. Biol. 13(4), e1005408 (2017)CrossRefGoogle Scholar
  13. 13.
    Glasser, M.F., et al.: Others: a multi-modal parcellation of human cerebral cortex. Nature 536(7615), 171–178 (2016)CrossRefGoogle Scholar
  14. 14.
    Glasser, M.F., et al.: Others: the minimal preprocessing pipelines for the Human Connectome Project. Neuroimage 80, 105–124 (2013)CrossRefGoogle Scholar
  15. 15.
    Guo, D., Arora, V., Amico, E., Goñi, J., Ventresca, M.: Dynamic generative model of the human brain in resting-state. In: Cherifi, C., Cherifi, H., Karsai, M., Musolesi, M. (eds.) Complex Networks & Their Applications VI, pp. 1271–1283. Springer International Publishing, Cham (2018)Google Scholar
  16. 16.
    Islam, M., et al.: A survey of graph based complex brain network analysis using functional and diffusional mri. Am. J. Appl. Sci. 14(12), 1186–1208 (2018)CrossRefGoogle Scholar
  17. 17.
    Jenkinson, M., Bannister, P., Brady, M., Smith, S.: Improved optimization for the robust and accurate linear registration and motion correction of brain images. Neuroimage 17(2), 825–841 (2002)CrossRefGoogle Scholar
  18. 18.
    Kolmogorov, A.N.: Three approaches to the quantitative definition of information. Int. J. Comput. Math. 2(1–4), 157–168 (1968)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Lempel, A., Ziv, J.: On the complexity of finite sequences. IEEE Trans. Infation Theory 22(1), 75–81 (1976)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Manson, S.M.: Simplifying complexity: a review of complexity theory. Geoforum 32(3), 405–414 (2001)CrossRefGoogle Scholar
  21. 21.
    Morzy, M., Kajdanowicz, T., Kazienko, P.: On measuring the complexity of networks: Kolmogorov complexity versus entropy. Complexity 2017 (2017)Google Scholar
  22. 22.
    Pastor-Satorras, R., Vespignani, A.: Complex networks: patterns of complexity. Nat. Phys. 6(7), 480 (2010)CrossRefGoogle Scholar
  23. 23.
    Piccinini, G., Scarantino, A.: Information processing, computation, and cognition. J. Biol. Phys. 37(1), 1–38 (2011)CrossRefGoogle Scholar
  24. 24.
    Rubinov, M., Sporns, O.: Complex network measures of brain connectivity: uses and interpretations. Neuroimage 52(3), 1059–1069 (2010)CrossRefGoogle Scholar
  25. 25.
    Ruffini, G.: An algorithmic information theory of consciousness. Neurosci. Conscious. 3(1) (2017)Google Scholar
  26. 26.
    Sato, J.R., Takahashi, D.Y., Hoexter, M.Q., Massirer, K.B., Fujita, A.: Measuring network’s entropy in adhd: a new approach to investigate neuropsychiatric disorders. Neuroimage 77, 44–51 (2013)CrossRefGoogle Scholar
  27. 27.
    Saxe, G.N., Calderone, D., Morales, L.J.: Brain entropy and human intelligence: a resting-state fmri study. PloS one 13(2), e0191,582 (2018)CrossRefGoogle Scholar
  28. 28.
    Shalizi, C.R., Crutchfield, J.P.: Computational mechanics: pattern and prediction, structure and simplicity. J. Stat. Phys. 104(3), 817–879 (2001)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Soler-Toscano, F., Zenil, H., Delahaye, J.P., Gauvrit, N.: Calculating kolmogorov complexity from the output frequency distributions of small turing machines. PLOS ONE 9(5), 1–18 (2014)CrossRefGoogle Scholar
  30. 30.
    Solomonoff, R.J.: A formal theory of inductive inference. Part I. Inf. Control. 7(1), 1–22 (1964)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Sporns, O.: Structure and function of complex brain networks. Dialogues Clin. Neurosci. 15(3), 247 (2013)Google Scholar
  32. 32.
    Stam, C.J., Reijneveld, J.C.: Graph theoretical analysis of complex networks in the brain. Nonlinear Biomed. Phys. 1(1), 3 (2007)CrossRefGoogle Scholar
  33. 33.
    Van Essen, D.C., et al.: Others: The WU-Minn human connectome project: an overview. Neuroimage 80, 62–79 (2013)Google Scholar
  34. 34.
    Viol, A., Palhano-Fontes, F., Onias, H., Araujo, D.B., Viswanathan, G.: Shannon entropy of brain functional complex networks under the influence of the psychedelic ayahuasca. Sci. Rep. 7(1), 7388 (2017)CrossRefGoogle Scholar
  35. 35.
    Wang, B., et al.: Decreased complexity in alzheimer’s disease: resting-state fmri evidence of brain entropy mapping. Front. Aging Neurosci. 9, 378 (2017)CrossRefGoogle Scholar
  36. 36.
    de Wit, L., Alexander, D., Ekroll, V., Wagemans, J.: Is neuroimaging measuring information in the brain? Psychon. Bull. Rev. 23(5), 1415–1428 (2016)CrossRefGoogle Scholar
  37. 37.
    Yao, Y., et al.: The increase of the functional entropy of the human brain with age. Sci. Rep. 3, 2853 (2013)CrossRefGoogle Scholar
  38. 38.
    Zenil, H., Hernández-Orozco, S., Kiani, N., Soler-Toscano, F., Rueda-Toicen, A., Tegnér, J.: A decomposition method for global evaluation of shannon entropy and local estimations of algorithmic complexity. Entropy 20(8), 605 (2018)CrossRefGoogle Scholar
  39. 39.
    Zenil, H., Kiani, N.A., Tegnér, J.: Quantifying loss of information in network-based dimensionality reduction techniques. J. Complex Netw. 4(3), 342–362 (2015)MathSciNetCrossRefGoogle Scholar
  40. 40.
    Zenil, H., Kiani, N.A., Tegner, J.: Methods of information theory and algorithmic complexity for network biology. Semin. Cell Dev. Biol. 51, 32–43 (2016)CrossRefGoogle Scholar
  41. 41.
    Zenil, H., Soler-Toscano, F., Dingle, K., Louis, A.A.: Correlation of automorphism group size and topological properties with program-size complexity evaluations of graphs and complex networks. Phys. A Stat. Mech. Its Appl. 404, 341–358 (2014)MathSciNetCrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.School of Industrial EngineeringPurdue UniversityWest LafayetteUSA

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