## 1 Introduction  
As an important supporting element, rolling bearings are widely used in various rotating machinery systems, such as wind turbines, aero engines and internal combustion engines. A minor bearing fault may affect the operation of the whole rotating machinery. Moreover, bearing faults can cause huge economic losses or even casualties [1; 2; 3]. With the rapid emerging and popularization of the Internet and the Internet of things, big data have brought revolutionary challenges and disruptive innovation to traditional information technology. Fault diagnosis has also entered the era of \"big data\" and fault recognition is an important part of it. The factors that cause bearing failure are numerous. The main causes of bearing failure include manufacturing and assembly faults which lead to vibrations dominated by out-of-balance shaft response and cage related frequencies [4]. Other modes of failure of bearings are initiated by contact conditions. Some are due to loss of the preload or interference fitting, which are known as the variable compliance effect [5]. Another major mode of failure in bearings is lubrication issues, lack of which can lead to wear, excessive friction and heat generation and scuffing. Finally, the worn rolling and sliding surfaces cause vibration, by which time any solution to the problem would be too late [6; 7; 8; 9]. Fault feature extraction and fault classification are two important aspects of bearing fault diagnosis. Using an effective fault feature extraction method to establish the fault feature vectors that fully reflect the fault information and selecting an advanced classifier to train and recognize the feature vectors are important to ensure the high precision of fault diagnosis. Many researches have been carried out on fault feature extraction of bearings. Wavelet packet decomposition was used to eliminate the noise of the signal and the fault features were extracted by ensemble empirical mode decomposition (EEMD) in Reference [10]. Successive wavelet decomposition techniques have also been used to focus on particular band of frequencies by obtaining the run-out wave attributed to particular features caused by the indicated sources, such as cage slipping, out-of-balance rotor rotation, etc. [11]. [PERSON] et al. [12] combined the time frequency distribution and the non-negative matrix factorization to enhance the bearing fault characterization. [PERSON] et al. [13] used the singular value and ratios of neighboring singular values to extract the fault features. In Reference [14], bearing fault features were extracted via singular spectrum analysis. [PERSON] et al. [15] utilized the hierarchical fuzzy entropy and Laplacian score to extract the fault signatures of bearings. [PERSON] et al. [16] proposed a neighborhood component analysis based feature extraction approach. [PERSON] et al. [17] proposed a method that combines Hilbert Huang transform (HHT) and singular value decomposition (SVD) to obtain the fault features of bearings. [PERSON] et al. [18] proposed an effective fault feature extraction approach by combining empirical mode decomposition (EMD) and SVD. In Reference [19], multi-scale permutation entropy (MPE) was used to extract fault features. In Reference [20] a fault feature extraction method based on EEMD, and multi-scale fuzzy entropy was proposed. These developed approaches are of great significance to fault diagnosis. However, some of them are proposed based on the signal decomposition methods, such as EMD, EEMD and wavelet decomposition. The EMD- and EEMD-based methods have modal aliasing problems which may affect the final identification results. A major limitation for the wavelet-based methods is that the analysis results are affected by the selection of wavelet basis functions. How to select wavelet basis functions adaptively is a difficult problem. Some other approaches belong to SVD and entropy based methods, whose effectiveness is easily affected by the parameter setting.