Functional deep echo state network improved by a bi-level optimization approach for multivariate time series classification

Abstract

The multivariate time series (MTS) classification is one of the major tasks of time series data mining. Many methods have been proposed to investigate the MTS classification. Among them, the method based on feature representation is the most popular and widely used one. However, there exist some shortcomings for this method, such as unsatisfactory accuracy, being sensitive to noise and not able to fully make use of time series data attributes. In order to overcome these disadvantages, we propose a new method called functional deep echo state network (FDESN) for MTS classification that utilizes two special operators: temporal aggregation and spatial aggregation. In general, the parameters of the FDESN are determined by random selection, human experience or trial and error. This may increase the complexity of the FDESN or reduce the accuracy of the FDESN. In this study, a novel bi-level optimization approach is proposed to optimize the parameters of the FDESN. The parameter selection problem in the FDESN is transformed into the bi-level optimization problem. The state transition algorithm (STA) is used to solve the bi-level optimization problem. Finally, the experimental results show that the proposed method is superior to other methods. In addition, the proposed method is successfully applied to anode condition identification in aluminum electrolysis. For the aluminum electrolysis datasets, the proposed method improved the average classification accuracy by about 3.5% compared with the other methods. For a specific aluminum electrolysis dataset ACS2504, the classification accuracy significantly increased from 77.92% to 82.69% by using the proposed method.