Dynamic topological data analysis (dynamic-TDA) focuses on analyzing dynamically changing time series data using persistent homology. The method can be applicable to wide variety of dynamically changing data including resting-state functional magnetic resonance images (rs-fMRI) and dynamically changing correlation matrices obtained from EEG. The basic terminology and concept are introduced in [1]. The package computes the Wasserstein distance between the collection of networks, perform topological clustering and topological inference.
The core tecchnique for dynamic-TDA is the topological distance between networks obtained through the Wasserstein distance, which was introduced in [2], [3].
For topological clustering using the Wasserstein distance, run SIMULATION_cluster.m. It is based on the core function WS_cluster.m. The method is explained in [4].
For topological inference, run SCRIPT.m. The new code WS_pdist2.m replaces pervious WS_distancemat.m that is extremly slow due to the use fo double-loops. The new code should be thousand times faster for large-scale network comparisions. The method is explained in [5].
[1] Songdechakraiwut, T. Chung, M.K. 2020 Dynamic topological data analysis for functional brain signals, IEEE International Symposium on Biomedical Imaging (ISBI) Workshop 1-4 Shorter abstract
[2] Songdechakraiwut, T., Shen, L., Chung, M.K. 2021 Topological learning and its application to multimodal brain network integration, Medical Image Computing and Computer Assisted Intervention (MICCAI), LNCS 12902:166-176
[3] Songdechakraiwut, T. Chung, M.K. 2022 Topological learning for brain networks, Annals of Applied Statistics arXiv: 2012.00675
[4] Chung, M.K., Huang, S.-G., Carroll, I.C., Calhoun, V.D., Goldsmith, H.H. 2023 Topological State-Space Estimation of Functional Human Brain Networks, arXiv:2201:00087.
[5] Moo K. Chung, Camille Garcia Ramos, Felipe Branco De Paiva, Jedidiah Mathis, Vivek Prabharakaren, Veena A. Nair, Elizabeth Meyerand, Bruce P. Hermann, Jeffery R. Binder, Aaron F. Struck, 2023 Unified Topological Inference for Brain Networks in Temporal Lobe Epilepsy Using the Wasserstein Distance, arXiv:2302.06673.
(C) 2022- Moo K. Chung University of Wisconsin-Madison mkchung@wisc.edu