Consistent and powerful graph-based change-point test for high-dimensional data

Significance Change-point detection in high-dimensional time series is necessary in many areas of science and engineering, including neuroscience, signal processing, network evolution, image analysis, and text analysis. In terms of a multivariate generalization of the Wald–Wolfowitz run test using the shortest Hamiltonian path, this paper proposes a distribution-free, consistent graph-based change-point detection for high-dimensional data. Once a change-point is detected, its location is estimated by using ratio cut. The test is very powerful against alternatives with a shift in mean or variance and is accurate in change-point estimation. Its applicability is demonstrated in the example of tracking cell division. A change-point detection is proposed by using a Bayesian-type statistic based on the shortest Hamiltonian path, and the change-point is estimated by using ratio cut. A permutation procedure is applied to approximate the significance of Bayesian-type statistics. The change-point test is proven to be consistent, and an error probability in change-point estimation is provided. The test is very powerful against alternatives with a shift in variance and is accurate in change-point estimation, as shown in simulation studies. Its applicability in tracking cell division is illustrated.