Abstract
Most of time series deriving from complex systems in real life is non-stationary, where the data distribution would be influenced by various internal/external factors such that the contexts are persistently changing. Therefore, the concept drift detection of time series has practical significance. In this paper, a novel method called online entropy-based time domain feature extraction (ETFE) for concept drift detection is proposed. Firstly, the empirical mode decomposition based on extrema symmetric extension is used to decompose time series, where features in various time scales can be adaptively extracted. Meanwhile, the end point effect caused by traditional empirical mode decomposition can be avoided. Secondly, by using the entropy calculation, the time-domain features are coarse-grained to quantify the structure and complexity of the time series, among which six kinds of entropy are used for discussion. Finally, a statistical process control method based on generalized likelihood ratio is used to monitor the change of the entropy, which can effectively track the mean and amplitude of the time series. Therefore, the early alarm of concept drift can be given. Synthetic data sets and neonatal electroencephalogram (EEG) recordings with seizures annotations data sets are used to validate the effectiveness and accuracy of the proposed method.
Highlights
The study of time series has strong theoretical significance and application value in real life.Due to its practical importance, the works related to the applications of time series are widely used in finance, engineering, medicine, and other fields [1,2,3,4]
In order to deal with the influence of time dependence of time series on concept drift detection, Guajardo [25] proposed a support vector machine regression model based on seasonal pattern to predict time series
The proposed method mainly consists of three parts: firstly, an empirical mode decomposition (EMD) based on extrema symmetric extension is used to decompose the original time series; secondly, the features of intrinsic mode functions (IMFs) in different time scales are calculated by using entropies; thirdly, the IMF-Entropy values are monitored by a generalized likelihood ratio (GLR)-based statistical control process algorithm such that the occurrence of concept drift can be detected
Summary
The study of time series has strong theoretical significance and application value in real life. X and its corresponding label Y, and the implicit detection methods are to track the change of the sample data distribution P(X) [5] From another point of view, explicit detection methods usually need base-learners to deal with classification problems, and directly determine the occurrence of drifts by monitoring whether the performance indicators of base learner classification (such as classification error rate) reach a threshold [10,11,12]. In order to detect the changes, a generalized likelihood ratio (GLR) based statistical process control algorithm [22] is used This method calculates the statistical characteristics of the data in each sliding window and compares with a given threshold to judge the breakpoint, so as to determine the location of the concept drift. The rest of the paper is organized as follows: The second part presents the literature review; the third part is the introduction of the proposed algorithm entropy-based time domain feature extraction (ETFE), where the principle and implementation are included; the fourth part is the related experiments, which include the performance evaluation of the proposed method in synthetic data and real data; the fifth part is the conclusion and prospect of our work
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