  Topological data analysis (TDA) provides a set of data analysis tools for
extracting embedded topological structures from complex high-dimensional
datasets. In recent years, TDA has been a rapidly growing field which has found
success in a wide range of applications, including signal processing,
neuroscience and network analysis. In these applications, the online detection
of changes is of crucial importance, but this can be highly challenging since
such changes often occur in a low-dimensional embedding within high-dimensional
data streams. We thus propose a new method, called PERsistence diagram-based
ChangE-PoinT detection (PERCEPT), which leverages the learned topological
structure from TDA to sequentially detect changes. PERCEPT follows two key
steps: it first learns the embedded topology as a point cloud via persistence
diagrams, then applies a non-parametric monitoring approach for detecting
changes in the resulting point cloud distributions. This yields a
non-parametric, topology-aware framework which can efficiently detect online
changes from high-dimensional data streams. We investigate the effectiveness of
PERCEPT over existing methods in a suite of numerical experiments where the
data streams have an embedded topological structure. We then demonstrate the
usefulness of PERCEPT in two applications in solar flare monitoring and human
gesture detection.
