As a key preprocessing step in classification, feature selection involves two conflicting objectives: maximizing the classification accuracy and minimizing the number of selected features. Therefore, multi-objective optimization is widely used in feature selection due to its excellent trade-off between the convergence of two objectives. However, most existing multi-objective feature selection methods still face the issues of the “curse of dimensionality” and high computational costs, especially when the search space is large. To solve the above issues, this paper proposes a bidirectional dynamic grouping multi-objective evolutionary approach for high-dimensional feature selection, referred to as BDGMOEA. This approach transforms a high-dimensional feature selection problem into a feature selection task with a smaller search space by the idea of feature grouping, in which one bit of an individual represents a group of features. Specifically, a grouping search strategy is developed to divide the features into different quadrants according to the importance of the features obtained by different evaluation techniques. Then, the features in each quadrant are grouped by sector. This strategy can effectively narrow the search space and quickly locate promising feature regions. In addition, a bidirectional dynamic adjustment mechanism is presented by considering the evolutionary state of the population, and it can be used to explore each feature in more detail and comprehensively to prevent good features from being ignored in unselected groups. The experimental results demonstrate that the proposed BDGMOEA method performs the best in most cases, indicating that BDGMOEA not only achieves better classification performance but also reduces the training time.

An echo state network (z) can provide an efficient dynamic solution for predicting time series problems. However, in most cases, ESN models are applied for predictions rather than classifications. The applications of ESN in time series classification (TSC) problems have yet to be fully studied. Moreover, the conventional randomly generated ESN is unlikely to be optimal because of the randomly generated input and reservoir weights, which are not always guaranteed to be optimal. Randomly generating all layer weights is improper, because a purely random layer might destroy the useful features. To overcome this disadvantage, this study provides a new input weight establishment framework of ESN based on autoencoder (AE) theory for TSC tasks. A global reversible AE (GRAE) algorithm is proposed to reestablish the random initialization input weights of the ESN. In existing ESN-AEs, the output weights obtained in the encoding process are directly reused as the initial input weights. By contrast, in GRAE, the reservoir layer with a reversible activation function is calculated by pulling the decoding layer output back and injecting it into the reservoir layer. Thus, feature learning is enriched by additional information, which results in improved performance. The current weights of the encoding layer are iteratively replaced by the decoding layer to ensure that the outputs of the GRAE are remarkably correlated with the input data. Visualization analyses and experiments of the input weights on a massive set of UCR time series datasets indicate that the proposed GRAE method can considerably improve the original two-layer ESN-based classifiers and the proposed GRAE-ESN classifier yields better performance compared with traditional state-of-the-art TSC classifiers. Furthermore, the proposed method can provide comparable performance and considerably faster training speed compared with three deep learning classifiers.