Title: Persistence Diagrams with Linear Machine Learning Models,
Abstract: 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.