The package computes the Wasserstein distance between the collection of networks, perform topological clustering, topological inference and topological embedding
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
[1] 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.
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
[2] 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.
The Wassersteind distance for graphs is explained in
[3] Songdechakraiwut, T. Chung, M.K. 2022 Topological learning for brain networks, Annals of Applied Statistics arXiv: 2012.00675
[4] 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
(C) 2022- Moo K. Chung University of Wisconsin-Madison [email protected]