Change Point Detection Based On Mann Whitney Statistics

With the development of science and technology,change point detection has become a research topic that many scholars attach importance to.It also plays an important role in the prediction and detection of meteorological field,brain electrocardiogram in medical field,human behavior,economy and finance,network security,industrial production and other aspects.The change point is the critical point when the two states of the system change,and in practice,the change of the system state is generally reflected by the change of a parameter s in the system.The research of change point detection is based on the time sequence S composed of the observed values of the parameter s in a period of time.If the parameter s changes at a certain time,the time sequence S changes at the corresponding time.The research of change point detection is to determine whether the sequence S changes and the position of the change,which is the position of the change point.Mann Whitney statistics is a kind of statistics used in Mann Whitney U hypothesis test.It can judge whether there are differences between two random variables,which is in line with the idea of change point detection.According to the properties of Mann Whitney statistics,this paper designs a change point detection algorithm based on sliding window.In addition,the method of obtaining control threshold and the strategy of detecting change point are designed.Combined with the statistical properties of Mann Whitney statistics,this paper proves that the consistency of the two sliding window lengths will minimize the variance of Mann Whitney statistics and reduce the interference of change point detection.In addition,this paper obtains the optimal sliding window length in two change point detection scenarios through simulation experiments.In the control threshold acquisition method,this paper compares the influence of Gauss method and Gev method on the detection performance of change point algorithm in online and offline scenes,and analyzes the advantages and disadvantages of the two methods in the two scenes.By comparing with other algorithms,the algorithm designed in this paper inherits the advantages of nonparametric change point detection algorithm.In nonparametric algorithms,the performance of offline change point detection is lower than that of comparison algorithm.In online change point detection,although the alarm rate of the algorithm designed in this paper is lower,the value of ARL is lower than other algorithms.In addition,the algorithm uses a fixed control threshold to adapt to the change point in each position of sequence S,while the control threshold in the comparison algorithm will change with the change point position.Finally,combined with the definition of s AUC,it is introduced into the field of change point detection as an improvement of Mann Whitney statistics.Compared with the original algorithm,s AUC can improve the detection accuracy of off-line change point detection,but it brings greater error in predicting the location of change points.