Brain activity: Conditional dissimilarity and persistent homology

There is an urgent need for reliable methods to compare brain activity networks, to distinguish between normal and abnormal functioning. A new approach is emerging based on Persistent Homology, which requires measuring distance between network nodes. We develop a new distance measure for autocorrelated time series, allowing network architectural analysis via persistent homology. The method jointly accounts for spurious spatial correlations, temporal correlations, and dimensionality issues arising from short temporal sampling compared to a larger number of network interactions. We demonstrate the new method on real resting state fMRI data and show improved results over correlation-based distance measures.