  Topological Data Analysis (TDA) is a rapidly growing field, which studies
methods for learning underlying topological structures present in complex data
representations. TDA methods have found recent success in extracting useful
geometric structures for a wide range of applications, including protein
classification, neuroscience, and time-series analysis. However, in many such
applications, one is also interested in sequentially detecting changes in this
topological structure. We propose a new method called Persistence Diagram based
Change-Point (PD-CP), which tackles this problem by integrating the widely-used
persistence diagrams in TDA with recent developments in nonparametric
change-point detection. The key novelty in PD-CP is that it leverages the
distribution of points on persistence diagrams for online detection of
topological changes. We demonstrate the effectiveness of PD-CP in an
application to solar flare monitoring.
