## 1 Introduction
As one of the important research contents in pattern recognition and data mining, clustering analysis plays a vital role in identifying the intrinsic structure of data and is widely used in many fields such as biology, economics, medicine, computer science, and so on [25; 26; 27]. The k-means algorithm and fuzzy c-means (FCM) algorithm are the two most famous clustering algorithms of this type. Compared with the k-means algorithm, the introduction of fuzzy information in the FCM algorithm makes the division of data samples more flexible, thus gaining wider attention [28; 29]. In the past years, based on the FCM algorithm, many scholars have proposed many improved FCM from various aspects and have achieved a series of new research results [30; 31; 32; 33]. These publications have achieved a lot of positive results in fault diagnosis, but there are still some problems. On the one hand, the vibration signals on the surface of machinery and equipment often contain sufficient information about the running status of parts. At the same time, because of the complexity of the working process of equipment, the vibration signals have obvious nonstationarity, and the dynamic signals and characteristic parameters of most equipment are often ambiguous. Thus, the differences in evaluation and discrimination between objective things are indistinct. So, the operating state can only be estimated in a specified range. On the other hand, many scholars have successfully improved the traditional FCM algorithm and achieved good results, but there are also some limitations, which are as follows. (1) Fuzziness exists at any sample point, which makes these improved methods vulnerable to noise and outliers. Additionally, the algorithm lacks robustness and the extensiveness of the algorithm is not obvious. (2) It is easy to lead to the equipotential partition of data, and it is greatly affected by uneven sampling and differences in the distribution characteristics of different data clusters. These two reasons lead to unsatisfactory results in fault diagnosis using the machine learning algorithm. Based on the analysis of the latest research progress, a fault diagnosis method based on ensemble empirical mode decomposition, permutation entropy, and Gath-Geva (GG) clustering is proposed in this paper. Firstly, the vibration signal of the rolling bearing is decomposed by the EEMD method,and then the permutation entropy value is calculated. For the obtained entropy feature vector, which has a high dimension and the data cannot be visualized, linear discriminant analysis (LDA) is used for dimensionality reduction. Since the data collected in the actual project is unlabeled data, the Gath-Geva clustering, as an improvement of the FCM clustering algorithm and Gustafson-Kessel (GK) clustering algorithm, is used for fault identification. The example of fault diagnosis shows that the method can effectively diagnose the fault of the bearing. The remaining part of this paper is organized as follows. Section 2 is about methods. In Section 2.1, the EEMD algorithm is introduced and discussed. Section 2.2 introduces the permutation entropy. The Gath-Geva clustering algorithm is discussed in Section 2.3. In Section 2.4, the steps and description of the proposed fault diagnosis method are described in detail. A clustering evaluation index is introduced in Section 2.5. Section 3 provides the data experiment of the proposed method. The analysis of the results is presented in Section 4. Finally, the conclusions are drawn in Section 5.