Topological Statistics

When we apply TDA to practical problems, it often becomes necessary to verify the reliability, classification, and the extraction of features for persistence diagrams. We have started to construct a theoretical and computational framework for topological statistics by developing standard statistical tools such as bootstrap and kernel methods for TDA.

literature

• G. Kusano, K. Fukumizu, and Y. Hiraoka. Kernel method for persistence diagrams via kernel embedding and weight factor. Journal of Machine Learning Research 18 (2018) 1–41.
• G. Kusano, K. Fukumizu, and Y. Hiraoka. Persistence weighted Gaussian kernel for topological data analysis. Proceedings of the 33rd International Conference on Machine Learning, New York, USA, MLR: W&CP (2016), 48. 2004–2013. (arXiv:1601.01741).
• I. Obayashi, Y. Hiraoka, M. Kimura. Persistence Diagrams with Linear Machine Learning Models. J. Appl. and Comput. Topology (2018), 1, 421–449.