The tutorial introduces a data-driven topological data analysis (TDA) framework, designed to elucidate the state spaces in dynamically changing functional brain networks. This educational session will guide participants through fundamental concepts of TDA, moving towards a comprehensive understanding of how topological distance can be leveraged to cluster brain networks into distinct states without models. Special attention will be given to the incorporation of the temporal dimension of brain network data, utilizing the scalability of Wasserstein distance to provide a more nuanced analysis of network changes over time. Participants will gain in-depth experience with this method, learning why it is advantageous over traditional methods such as k-means clustering for estimating state spaces. The tutorial will delve into the intriguing investigation of if TDA is sensitive and flexible enough to determine the heritability of state changes. The tutorial is based on arXiv:2201.00087 (PLOS Computational Biology).
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