MINDS Seminar Series | Ippei Obayashi (RIKEN) - A Framework for Machine Learning with Persistent Homology

Persistent homology (PH) enables us to summarize the shape of data quantitatively and effectively by using the mathematical concept of topology. To capture the characteristic geometric structure of the data, various PH-machine learning methods are proposed. Our research group also proposed a framework for machine learning with PH. In this talk, I will present our framework. I will also present an application of our framework to materials research.

The outline of the framework is as follows:

1. Persistence Image, a simple persistence diagram vectorization method, is used
2. Linear machine learning models such as linear regression, logistic regression, PCA, or NMF are used
3. Learned geometric structures are mapped on the original data by using "inverse analysis"

The framework mainly focuses on the interpretability of learned results.

The researches in this talk are published in the following two papers: * Ippei Obayashi, Yasuaki Hiraoka, and Masao Kimura. Persistence diagrams with linear machine learning models. Journal of Applied and Computational Topology 1, 3-4, 421–449, (2018). * Akihiko Hirata, Tomohide Wada, Ippei Obayashi and Yasuaki Hiraoka. Structural changes during glass formation extracted by computational homology with machine learning. Communications Materials 1, 98 (2020). https://doi.org/10.1038/s43246-020-00100-3