A WSFA-based adaptive feature extraction method for multivariate time series prediction

In recent years, artificial neural networks (ANNs) have been successfully and widely used in multivariate time series prediction, but the accuracy of the prediction is significantly affected by the ANNs' input. In order to determine the appropriate input for more accurate prediction, a weighted slow feature analysis-based adaptive feature extraction (WSFA-AFE) method is proposed for multivariate time series prediction. Firstly, the weighted SFA (WSFA) algorithm is developed to extract slow features weighted by their contributions. Then, an improved adaptive sliding window algorithm is designed to self-determine the historical information of slow features for input. Finally, the out-of-model performance of the WSFA-AFE method is verified by applying it to different ANN models with several benchmark data sets as well as a practical dataset in wastewater treatment process. The results indicate that a better modeling performance of ANNs for multivariate time series prediction can be obtained by the WSFA-AFE method, which can adaptively extract feature variables from the multivariate time series. Besides, the robustness of the proposed method is demonstrated as well.