Quasi-Periodicity Detection via Repetition Invariance of Path Signatures.

Periodicity or repetition detection has a wide varieties of use cases in human activity tracking, music pattern discovery, physiological signal monitoring and more. While there exists a broad range of research, often the most practical approaches are those based on simple quantities that are conserved over periodic repetition, such as auto-correlation or Fourier transform. Unfortunately, these periodicity-based approaches do not generalise well to quasi-periodic (variable period) scenarios. In this research, we exploit the time warping invariance of path signatures to find linearly accumulating quantities with respect to quasi-periodic repetition, and propose a novel repetition detection algorithm Recurrence Point Signed Area Persistence. We show that our approach can effectively deal with repetition detection with period variations, which similar unsupervised methods tend to struggle with.