Skip to main content
SpringerLink
Log in

Using Algorithmic Complexity to Differentiate Cognitive States in fMRI

  • Conference paper
  • First Online:
Complex Networks and Their Applications VII (COMPLEX NETWORKS 2018)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 813))

Included in the following conference series:

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  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. Amico, E., Goñi, J.: The quest for identifiability in human functional connectomes. Sci. Rep. 8(1), 8254 (2018)

    Article  Google Scholar 

  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. Betzel, R.F., Bassett, D.S.: Generative models for network neuroscience: prospects and promise. J. R. Soc. Interface 14(136), 20170623 (2017). https://doi.org/10.1098/rsif.2017.0623

  5. Bonmati, E., Bardera, A., Feixas, M., Boada, I.: Novel brain complexity measures based on information theory. Entropy 20(7), 491 (2018)

    Article  Google Scholar 

  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. 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)

    Article  Google Scholar 

  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. Chaitin, G.J.: On the length of programs for computing finite binary sequences: statistical considerations. J. ACM 16(1), 145–159 (1969)

    Article  MathSciNet  Google Scholar 

  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)

    MATH  Google Scholar 

  11. Fornito, A., Zalesky, A., Breakspear, M.: Graph analysis of the human connectome: promise, progress, and pitfalls. Neuroimage 80, 426–444 (2013)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  13. Glasser, M.F., et al.: Others: a multi-modal parcellation of human cerebral cortex. Nature 536(7615), 171–178 (2016)

    Article  Google Scholar 

  14. Glasser, M.F., et al.: Others: the minimal preprocessing pipelines for the Human Connectome Project. Neuroimage 80, 105–124 (2013)

    Article  Google Scholar 

  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. 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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  18. Kolmogorov, A.N.: Three approaches to the quantitative definition of information. Int. J. Comput. Math. 2(1–4), 157–168 (1968)

    Article  MathSciNet  Google Scholar 

  19. Lempel, A., Ziv, J.: On the complexity of finite sequences. IEEE Trans. Infation Theory 22(1), 75–81 (1976)

    Article  MathSciNet  Google Scholar 

  20. Manson, S.M.: Simplifying complexity: a review of complexity theory. Geoforum 32(3), 405–414 (2001)

    Article  Google Scholar 

  21. Morzy, M., Kajdanowicz, T., Kazienko, P.: On measuring the complexity of networks: Kolmogorov complexity versus entropy. Complexity 2017 (2017)

    Google Scholar 

  22. Pastor-Satorras, R., Vespignani, A.: Complex networks: patterns of complexity. Nat. Phys. 6(7), 480 (2010)

    Article  Google Scholar 

  23. Piccinini, G., Scarantino, A.: Information processing, computation, and cognition. J. Biol. Phys. 37(1), 1–38 (2011)

    Article  Google Scholar 

  24. Rubinov, M., Sporns, O.: Complex network measures of brain connectivity: uses and interpretations. Neuroimage 52(3), 1059–1069 (2010)

    Article  Google Scholar 

  25. Ruffini, G.: An algorithmic information theory of consciousness. Neurosci. Conscious. 3(1) (2017)

    Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  28. Shalizi, C.R., Crutchfield, J.P.: Computational mechanics: pattern and prediction, structure and simplicity. J. Stat. Phys. 104(3), 817–879 (2001)

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  30. Solomonoff, R.J.: A formal theory of inductive inference. Part I. Inf. Control. 7(1), 1–22 (1964)

    Article  MathSciNet  Google Scholar 

  31. Sporns, O.: Structure and function of complex brain networks. Dialogues Clin. Neurosci. 15(3), 247 (2013)

    Google Scholar 

  32. Stam, C.J., Reijneveld, J.C.: Graph theoretical analysis of complex networks in the brain. Nonlinear Biomed. Phys. 1(1), 3 (2007)

    Article  Google Scholar 

  33. Van Essen, D.C., et al.: Others: The WU-Minn human connectome project: an overview. Neuroimage 80, 62–79 (2013)

    Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  37. Yao, Y., et al.: The increase of the functional entropy of the human brain with age. Sci. Rep. 3, 2853 (2013)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

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.

Author information

Authors and Affiliations

  1. School of Industrial Engineering, Purdue University, West Lafayette, IN, 47907, USA

    Mario Ventresca

Authors
  1. Mario Ventresca
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mario Ventresca .

Editor information

Editors and Affiliations

  1. Nokia Bell Labs, Cambridge, UK

    Luca Maria Aiello

  2. IUT Lumière, University of Lyon, Bron Cedex, France

    Chantal Cherifi

  3. LE2I UMR CNRS 6306 9, University of Burgundy, Dijon Cedex, France

    Hocine Cherifi

  4. Mathematical Institute, University of Oxford, Oxford, UK

    Renaud Lambiotte

  5. Department of Computer Science and Technology, The Computer Laboratory, University of Cambridge, Cambridge, UK

    Pietro Lió

  6. Center for Complex Networks and Systems Research, School of Informatics, Computing, and Engineering, Indiana University, Bloomington, IN, USA

    Luis M. Rocha

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Ventresca, M. (2019). Using Algorithmic Complexity to Differentiate Cognitive States in fMRI. In: Aiello, L., Cherifi, C., Cherifi, H., Lambiotte, R., Lió, P., Rocha, L. (eds) Complex Networks and Their Applications VII. COMPLEX NETWORKS 2018. Studies in Computational Intelligence, vol 813. Springer, Cham. https://doi.org/10.1007/978-3-030-05414-4_53

Download citation

Publish with us

Policies and ethics

Search

Navigation