# Time Series Feature Selection Method Based on Mutual Information
## 1 Introduction  
Time series data mining has extensive and important applications in the field of machine learning, such as data classification, clustering, or prediction, which can help explore the potential patterns in time series data that are useful for subsequent research. Currently, most researchers mainly focus on the processing of univariate time series. However, with the development of data collection technology, multidimensional time series data have become increasingly common and contain a large amount of potentially valuable information. Feature selection is an important step in data processing of high-dimensional data (such as regression and classification). Its main function is to reduce computational complexity, avoid the \"curse of dimensionality\" problem [1], reduce training time, and improve the performance of the predictor [2]. Therefore, how to effectively extract system features is one of the key issues in the field of time series analysis [3], which has been widely used in the following fields: image recognition [4; 5], natural language processing [6; 7], data mining [8; 9], fault diagnosis [10; 11; 12], remaining useful life prediction [13; 14], microbes classification [15], fatigue detection [16], image classification [17], intrusion detection [18; 19; 20; 21], etc. Feature selection methods can be roughly divided into three categories [22] including filter, wrapper, and embedded, according to their relationship with learning methods [23; 24]. On the other hand, according to the utilized training data, feature selection methods can be divided into supervised [25], unsupervised, and semi-supervised models [26]. In this paper, we focus on the feature selection of time series. At present, the feature selection of time series, in most cases, is mainly conducted by observing the variable trends, amplitude, noise, and other characteristics [27]. This kind of method has problems such as strong subjectivity, inability to conduct quantitative analysis, and inaccuracy. To solve these problems, we propose a time series feature extraction method based on mutual information. Mutual information is a measure of the interdependence between two variables, which indicates how much information is shared between two variables [28]. The greater the mutual information between variables, the stronger the correlation. Firstly, we determine the correlation between features and then select features with a strong correlation with the target variable. This is an unsupervised feature selection method and has become an important feature selection method [29]. In combination with other methods, MI-based feature selection has derived many other methods, such as MI with a correlation coefficient [30], variance impact factor [31], fisher score [32], binary butterfly optimization algorithm [33], conditional mutual information [34], deep neural network [35; 36], etc. Among them, the authors of [37] proposed a deep generative network model for feature extraction of multivariate time series and introduced mutual information into the loss function to improve the expression capability and accuracy of the model. In the study [31], the authors proposed a variable selection method based on mutual information and the variance inflation factor (MI-VIF), which eliminated the variables based on MI and VIF, respectively, and showed good prediction performance. A feature selection algorithm based on MI and particle swarm optimization, which optimized the traditional particle update mechanism and swarm initialization strategy, was proposed in the work [23]. The study [38] proposed a novel fuzzy multi-information-based multi-label feature selection approach that was suitable for multi-label learning. The authors of [39] proposed a conditional multiple information-based feature selection algorithm for maximum reliability and minimum redundancy. The above research mainly focuses on the improvement of the feature extraction algorithm based on mutual information.