Continuation of Point Cloud Data via Persistence Diagram (Inverse Problem)

The correspondence from point cloud data to persistence diagrams is differentiable under certain conditions. Hence, by using the implicit function theorem, we can trace the point cloud data to a new one that attains a slightly deformed persistence diagram from the original. We have been developing an inverse problem scheme by combining this idea with the continuation method studied in bifurcation theory of dynamical systems.

literature

• M. Gameiro, Y. Hiraoka, I. Obayashi. Continuation of Point Clouds via Persistence Diagrams. Physica D: Nonlinear Phenomena 334, 118-132 (2016).