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.