## 1 Introduction  
With technological advancement and industrial development, the scale of data has significantly grown and data imbalance has become a typical characteristic. Both internal and external factors can cause data imbalance. For example, in the first case, illegal and other abnormal videos only account for a small portion of internet video traffic [1], there are far fewer customers with bad credit than with good credit [2], and there are far fewer people suffering from breast cancer than healthy people [3]. The second case includes unexpected interruptions in the balanced data transmission to a database [4]. A current trend is to use machine learning methods to mine potential and hidden information from data to provide more intelligent services. Traditional classification algorithms usually assume a balanced number of samples in different categories and consistent misclassification costs for all categories. However, it is well known that patient samples are few, and their misclassification cost is much higher than that of healthy people [5]; and a high-quality production process may also produce some substandard products, whose potential cost, if they enter the market, is higher [6]. As can be seen, these assumptions are difficult to satisfy in real applications, and imbalanced data may degrade classification performance, which is specifically manifested in high overall classification accuracy, low classification accuracy of minority classes, and high overall misclassification cost. Many imbalanced data classification methods have emerged at the data, algorithm, and ensemble learning levels. From the perspective of data distribution, data-level methods use resampling to reduce the imbalance of datasets, and can be divided into undersampling and oversampling methods. Algorithm-level methods improve performance by improving the learning process and paying more attention to minority-class samples, including cost-sensitive learning, one class learning methods, and feature methods. Ensemble learning methods are usually combined with data- or algorithm-level methods. With the rapid development of deep networks, some methods combining ensemble learning and deep neural networks have also been proposed in recent years, which can be used to solve the imbalanced data classification problem [7; 8]. Most studies have used one or two methods to improve the performance of imbalanced data classification algorithms [9; 10; 11]. [PERSON] et al. pointed out that pre-extracted feature variables, which might be sub-optimal for subsequent classifier learning, would reduce classification performance [12]. For this reason, it is necessary to incorporate different levels of processing, such as feature extraction and algorithm improvement, into a unified pattern-recognition framework for training. Unlike traditional machine learning classification algorithms, the MTS is a pattern-recognition technique requiring no data distribution assumptions [13]. The method combines the Mahalanobis distance (MD) for anomaly detection and the Taguchi's method for feature selection. [PERSON] et al. pointed out that the MTS is one of the most robust techniques for imbalanced data classification problems, and used it to construct a pressure ulcer prediction model, which showed high accuracy [14]. [PERSON] et al. applied the MTS to rotating machinery fault diagnosis and showed that the higher the imbalance ratio of the data, the more significant the difference in the classification performance of the MTS compared with support vector machine, random forest, and their cost-sensitive implementations [15]. Although the imbalanced data classification performance of the MTS has been high, its feature selection and threshold determination methods still lack a complete theoretical statistical foundation [16]. In view of this, researchers have optimized the imbalanced data classification performance of the MTS in several aspects.