  Topological Data Analysis (TDA) is a rising field of computational topology
in which the topological structure of a data set can be observed by persistent
homology. By considering a sequence of sublevel sets, one obtains a filtration
that tracks changes in topological information. These changes can be recorded
in multi-sets known as {\it persistence diagrams}. Converting information
stored in persistence diagrams into a form compatible with modern machine
learning algorithms is a major vein of research in TDA. {\it Persistence
curves}, a recently developed framework, provides a canonical and flexible way
to encode the information presented in persistence diagrams into vectors. In
this work, we propose a new set of metrics based on persistence curves. We
prove the stability of the proposed metrics. Finally, we apply these metrics to
the UCR Time Series Classification Archive. These empirical results show that
our metrics perform better than the relevant benchmark in most cases and
warrant further study.
