  We introduce a novel geometry-oriented methodology, based on the emerging
tools of topological data analysis, into the change point detection framework.
The key rationale is that change points are likely to be associated with
changes in geometry behind the data generating process. While the applications
of topological data analysis to change point detection are potentially very
broad, in this paper we primarily focus on integrating topological concepts
with the existing nonparametric methods for change point detection. In
particular, the proposed new geometry-oriented approach aims to enhance
detection accuracy of distributional regime shift locations. Our simulation
studies suggest that integration of topological data analysis with some
existing algorithms for change point detection leads to consistently more
accurate detection results. We illustrate our new methodology in application to
the two closely related environmental time series datasets -ice phenology of
the Lake Baikal and the North Atlantic Oscillation indices, in a research query
for a possible association between their estimated regime shift locations.
