Persistent Homological State-Space Estimation of Functional Human Brain Networks at Rest

We present a new data driven topological data analysis (TDA) approach for estimating state spaces in dynamically changing human functional brain networks of human. Our approach penalizes the topological distance between networks and clusters dynamically changing brain networks into topologically distinct states. Our method takes into account the temporal dimension of the data through the Wasserstein distance between networks. Our method is shown to outperform the widely used k-means clustering often used in estimating the state space in brain networks. The method is applied to more accurately determine the state spaces of dynamically changing functional brain networks. Subsequently, we address the question of whether the overall topology of brain networks is a heritable feature using the twin study design. MATLAB code for the method is available at https://github.com/laplcebeltrami/PH-STAT.