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.