# Improving Bearing Fault Diagnosis Using Maximum Information Coefficient Based Feature Selection
## 1 Introduction
A correlation coefficient of two simplified neutrosophic sets (SNSs) was proposed to diagnose the bearing fault types by [PERSON] [19]. In [20], Laplacian Score (LS) for feature selection was utilized to refine the feature vector by sorting the features according to their importance and correlations. Besides, [PERSON] [21] employed the Decision Tree algorithm to select the important features of the time-domain signal, and the low correlation features was selected. [PERSON] [22] computed the mutual information (MI) of decomposed components and the original signal, and extracted the noiseless component, in order to obtain the reconstructed signal. However, in terms of relevance, researchers did not take relevance between features and fault categories into account in feature selection, only considering the correlation between features. The purpose of feature selection is not just simply reducing dimensions for the data. It is more about eliminating redundant and irrelevant features. Redundant features can be eliminated by the measurement of relevance among features. The stronger the relevance between two features, the stronger the redundancy and replaceability between them. Moreover, irrelevant features can be eliminated through the measurement of relevance between features and categories. The stronger the relevance between features and categories, the stronger the distinguishability of features from categories. Irrelevant and redundant features can be eliminated from a raw feature set according to relevance. Therefore, consideration of relevance plays an essential role in reducing data dimensions in feature selection. On the other hand, some work [8; 9; 10; 11; 12; 13] selected features based on wrapper methods and increased the computational complexity. To avoid the cost of searching, the idea of intersection or union operation was put forward to merge feature subsets [23; 24]. When it comes to the problem of coping with redundant information, principal component analysis (PCA) has been extensively studied. PCA is an algorithm that can effectively extract subsets from data by reducing the dimensions of the data set [25]. Since the principal component includes most information of the raw features which are irrelevant and do not contain redundant information, the principal component can be used to replace raw features. Based on this, PCA can realize data reduction and reduce the complexity of data processing, preventing dimensional disaster [26]. Typical PCA algorithms like those in [27; 28; 29; 30] are used to extract features and to reduce data dimensions. Based on the problems mentioned above, a novel feature selection method called FF-FC-MIC based on the Feature-to-Category-Maximum Information Coefficient is proposed. The main contributions of this paper are as follows:  
1. A new frame of feature selection is proposed for bearing fault diagnosis, which aims at considering the relevance among features and the relevance between features and fault categories. In the new feature selection frame, strong relevance features are eliminated by an FF-MIC matrix based on the relevance between features and features. On the contrary, strong relevance features are selected by the FC-MIC matrix based on the relevance between features and categories. The proposed frame can eliminate not only redundant features but also irrelevant features from the feature set. 2. In order to avoid computational complexity brought by wrapper methods, an intersection operation is applied to merge the obtained feature subsets. The intersection operation has advantages of forming a final subset with a lower dimension and saving time, instead of subset searching. 3. This paper applied two datasets to validate the effectiveness and adaptability of proposed method. It turned out the proposed method has a good applicability and stability. The remainder of this paper is organized as follows. Section 2 introduces the basic theory and algorithm applied in this paper. Section 3 gives the details of the proposed method. Section 4 shows the experimental results.