Study And Application Of Change-point Detection Of Time Series

As a typical kind of data,time series has been widely employed in various appli-cations.Recently,the research on time series has attracted more and more attentions.Especially,change-point detection of time series has become a popular research direc-tion of data analysis,which plays an important role in practical usages ranging from the analysis of electroencephalogram,video processing,machine condition monitor-ing,to name a few.This thesis focuses on two categories of time series:linear time series and non-linear time series,and addresses the problem of change-point detection.In the proposed schemes,the given time series is first modeled,and then its temporal anomalies are computed to quantitatively describe the structural fluctuation.Based on the resulting anomalies,change point or cycle is determined by the making decision.Finally,the performance of the proposed schemes is demonstrated by rich experiments in their typical applications.Change-point detection of linear time series is performed via one-dimensional anal-ysis and multidimensional analysis respectively.On the one hand,the linear time series is first mapped into an embedding space(i.e.,Reproducing Kernel Hilbert Space).In the embedding space,the Maximum Mean Discrepancy is employed to measure quan-titatively the temporal fluctuation.Thanks to an automatic technique with an employ-ment of level a,an adaptive threshold is generated for final change decision.Different from the one-dimensional analysis,the multidimensional analysis of time series takes account into the case that the information in each dimension will contribute the struc-tural change differently.Hence,in this thesis,a novel aggregating model is proposed for data modeling and the CUSUM statics is performed in each dimension separate-ly for anomaly computation.A fusion method based on weighted linear combination is then used to combine all anomalies.The change point is decided by a pre-defined threshold.Finally,this thesis performs the effectiveness of the proposed frameworks in key-frame selection of surveillance videos.As for the change-point detection of non-linear time series,we focus on the periodic time series.At first,the graph-based framework for change detection of fixed-periodic time series is reviewed.The graph model for data modeling is adopted to describe the information of each cycle.Meanwhile,a numerical method based on the spectrum analysis of adjacency matrix is proposed for computing temporal anomalies.Then the martingale-test is introduced for decision making.However,different from the fixed period of periodic time series,the quasi-periodic time series is often modulated in amplitude and/or frequency so that graph model can not be employed directly for its data modeling.For this purpose,a novel framework of cycle segmentation and normalization is proposed.The cycle segmentation includes two steps:starting-time calibration and cycle-length decision.When the ongoing cycle has been segmented,it is normalized as a common timing cycle by the interpolation and averaging operations.Meanwhile,this scheme designs a control time-line based on normal distribution to avoid over-segmentation during cycle segmentation and normalization.Based on the normalized quasi-periodic time series,the graph model is introduced into the change detection of quasi-periodic time series.The thesis addresses the problem of using the proposed algorithm for change-point detection for the purpose of rotating machinery monitoring under non-stationary operating conditions.Finally,we conclude the proposed studies,and discuss the future work along with the thesis.