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Topological data analysis (TDA) provides a set of data analysis tools forextracting embedded topological structures from complex high-dimensionaldatasets. In recent years, TDA has been a rapidly growing field which has foundsuccess in a wide range of applications, including signal processing,neuroscience and network analysis. In these applications, the online detectionof changes is of crucial importance, but this can be highly challenging sincesuch changes often occur in a low-dimensional embedding within high-dimensionaldata streams. We thus propose a new method, called PERsistence diagram-basedChangE-PoinT detection (PERCEPT), which leverages the learned topologicalstructure from TDA to sequentially detect changes. PERCEPT follows two keysteps: it first learns the embedded topology as a point cloud via persistencediagrams, then applies a non-parametric monitoring approach for detectingchanges in the resulting point cloud distributions. This yields anon-parametric, topology-aware framework which can efficiently detect onlinechanges from high-dimensional data streams. We investigate the effectiveness ofPERCEPT over existing methods in a suite of numerical experiments where thedata streams have an embedded topological structure. We then demonstrate theusefulness of PERCEPT in two applications in solar flare monitoring and humangesture detection.

PERCEPT: a new online change-point detection method using topological data analysis