Persistence Diagrams with Linear Machine Learning Models

Persistence diagrams have been widely recognized as a compact descriptor for characterizing multiscale topological features in data. When many datasets are available, statistical features embedded in those persistence diagrams can be extracted by applying machine learnings. In particular, the ability for explicitly analyzing the inverse in the original data space from those statistical features of persistence diagrams is significantly important for practical applications. In this paper, we propose a unified method for the inverse analysis by combining linear machine learning models with persistence images. The method is applied to point clouds and cubical sets, showing the ability of the statistical inverse analysis and its advantages. This work is partially supported by JSPS Grant-in-Aid 16K17638, JST CREST Mathematics15656429, JST “Materials research by Information Integration” Initiative (MI2I) project of the Support Program for Starting Up Innovation Hub, Structural Materials for Innovation Strategic Innovation Promotion Program D72, and New Energy and Industrial Technology Development Organization (NEDO). Ippei Obayashi Advanced Institute for Materials Research (WPI-AIMR), Tohoku University. 2-1-1 Katahira, Aoba-ku, Sendai, 980-8577 Japan Tel.: +81-22-217-6320 Fax: +81-22-217-5129 E-mail: [email protected] Y. Hiraoka Advanced Institute for Materials Research (WPI-AIMR), Tohoku University. Center for Materials research by Information Integration (CMI2), Research and Services Division of Materials Data and Integrated System (MaDIS), National Institute for Materials Science (NIMS). E-mail: [email protected]