Change Point Detection with Mean Shift Based on AUC from Symmetric Sliding Windows

Change point detection is widely used in signal detection, industrial engineering, economy, finance, biomedicine and many other fields. The widely used parametric methods require prior knowledge of the noise signal distribution, which are seldom realistic. In practice, when the distribution of noise is not known, it is desirable to design algorithms based on non-parametric statistics, which, in the null case (no change point), are completely distribution free. To this end, we propose to use two symmetric sliding windows to compute the Area Under the receiver operating characteristic Curve (AUC) as a test statistic to measure the difference between the distribution of two samples. In the stage of change point detection, a threshold is designed according to hypothesis test which is based on the null distribution of the test statistics. This threshold is used to detect the potential change points in the signal. To reduce the probability of false alarm detection, a key parameter K is set to distinguish and delete the false alarms in potential change points. Comparative studies showed that our proposed method outperforms the classical Relative unconstrained Least-Squares Importance Fitting (RuLSIF) algorithm and is also better than the Hawkins, Qiu, and Kang (HQK) algorithm when the noise follows non-normal distributions.

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