A Novel Method for Fast Change-Point Detection on Simulated Time Series and Electrocardiogram Data

Abstract

Although Kolmogorov-Smirnov (KS) statistic is a widely used method, some weaknesses exist in investigating abrupt Change Point (CP) problems, e.g. it is time-consuming and invalid sometimes. To detect abrupt change from time series fast, a novel method is proposed based on Haar Wavelet (HW) and KS statistic (HWKS). First, the two Binary Search Trees (BSTs), termed TcA and TcD, are constructed by multi-level HW from a diagnosed time series; the framework of HWKS method is implemented by introducing a modified KS statistic and two search rules based on the two BSTs; and then fast CP detection is implemented by two HWKS-based algorithms. Second, the performance of HWKS is evaluated by simulated time series dataset. The simulations show that HWKS is faster, more sensitive and efficient than KS, HW, and T methods. Last, HWKS is applied to analyze the electrocardiogram (ECG) time series, the experiment results show that the proposed method can find abrupt change from ECG segment with maximal data fluctuation more quickly and efficiently, and it is very helpful to inspect and diagnose the different state of health from a patient's ECG signal.

A KST framework for correlation network construction from time series signals

“…Not surprised, the method based on KST created the FCNs with smaller false positive and false negative rates than those from KS and T methods. It might be explained by that KST had better ability for detection of the fluctuations from each of the time series segments, which has been addressed in our previous work [19][20][21]. Some examples of the visualized FCNs are shown in figure 3.…”

“…A review of these algorithms can be found in [18]. In our previous study on time point change detection [19][20][21], we analyzed how KS and T could be used for calculating the fluctuations of a time series. In this study, we took the advantages of KS and T statistic for detection of the maximum fluctuations in the segments of a time series and built a fluctuation correlation network (FCN) based on the fluctuation data matrices that was created from a combined method with KS and T statistics (KST).…”

A WED Method for Evaluating the Performance of Change-Point Detection Algorithms

“…The normalized TPD, FND, TND and FPD can be represented as true positive distant rate (TPDR), positive error distance rate (PEDR), true negative distance rate (TNDR) and negative error distance rate (NEDR). These values can be calculated by formula (5) to formula (8). Basically, the distance between the start point and the t-CP and the distance from the t-CP to end point of each tested time series are both normalized to 1, and the normalized t-CP position for each time series will match to the same point.…”

“…This application would allow appropriate staff to be alerted of changes in a patient's medical situation and to provide on-time treatment [6,7]. CPD models utilize the algorithms that cover the fields of data mining, statistics, and computer science, including parametric and nonparametric methods [8,9,10,11]. Each CPD algorithm can be assessed from the aspect of detection accuracy, computational cost or whether it can be a real time detection.…”

“…A WED metrics is proposed to compare the overall performance of CPD models working across multiple time series of different lengths and the occurrence of t-CPs at different positions in the time series. The ability of this WED metric to evaluate different CPD models was tested on Kolmogorov-Smirnov (KS) [8,11], SSA [17,9] and T [18] algorithms that worked on the synthetic datasets in different sample sizes and different variances. The implementations of KS, SSA and T for CPD on time series were described in our previous studies [8,19].…”