Using Algorithmic Complexity to Differentiate Cognitive States in fMRI
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.
KeywordsAlgorithmic 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.Amico, E., Goñi, J.: Maximizing the individual fingerprints of human functional connectomes through decomposition into brain connectivity modes (2017). arXiv preprint arXiv:1707.02365
- 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
- 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
- 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
- 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
- 21.Morzy, M., Kajdanowicz, T., Kazienko, P.: On measuring the complexity of networks: Kolmogorov complexity versus entropy. Complexity 2017 (2017)Google Scholar
- 25.Ruffini, G.: An algorithmic information theory of consciousness. Neurosci. Conscious. 3(1) (2017)Google Scholar
- 31.Sporns, O.: Structure and function of complex brain networks. Dialogues Clin. Neurosci. 15(3), 247 (2013)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