# Fault Diagnosis of Rotating Electrical Machines Using Multi-Label Classification
## 2 Multiple Fault Classification and Fault Severity Determination  
### Brief Introduction of Multi-Label Classification Methods  
Modern industry requires data mining algorithms that are able to efficiently cope with the growing amount of information and large datasets. Specialized processing tasks of various practical application fields deal with common characteristics of the stored data that can be assigned to multiple categories [99; 100]. Therefore, multi-label classification algorithms have gained increasing interest in recent years. Specialized techniques for learning such type of data, which have the capability of predicting a set of relevant labels for new species, are still the focus of researches. Currently, three main groups of newly developed multi-label classification methods are proposed in the literature, namely the data transformation methods, adaptation methods, and ensemble of classifiers [101; 102]. Early solutions for multi-label classification methods cover the data transformation techniques. The concept is to turn the original multi-label set into binary sets or multi-class sets that adequately can be processed with the classical algorithms. Besides binarization with the widely applied binary relevance technique, also the voting methods and divide-and-conquer approaches are applied to accomplish multi-label transformation [100; 103; 104]. Such separated sets are learned by single-label classifiers, such as decision trees. This group also includes the Classifier Chains that are similar to the binary relevance technique but perform the binarization in consecutive classifiers, since the models' order has importance [105; 106]. The output of one response variable for a sub-classifier is used as an additional feature in the next sub-classifier. The optimal order of the classification models can be enhanced by the Naive Bayes method.  
Adaptation methods are based on the adaptation of conventional classification methods to multi-label versions without problem transformation. The adaptation methods are extensions of well-founded automatic classification algorithms. For instance, the support vector machine (SVM) classifiers [107], the k-nearest neighbors (KNN) [108], or temporal classifiers [109] are able to predict binary or multiclass outputs simultaneously [110; 111]. KNN is a non-parametric method used for classification and regression [112; 113]. In KNN, an object is classified through a plurality vote of its neighbors while the object assigned to the class of the most common k nearest neighbors. K is a positive and small number, to be able to reduce the number of calculations, and thus the process duration. Similarly, the neural networks and decision trees have such abilities, but the adaptation of the algorithm may become difficult. Ensemble classifiers are also held notable interest. The KNN employs an euclidean distance function (\(D_{rt}\)) as follows:  
\[D_{rt}=\sqrt{\sum_{i=1}^{m}W_{i}}(x_{ir}-x_{it})^{2},\ t=1,2,\ldots,\ n \tag{1}\]  
where \(W_{i}\)(\(i=1,2,\ldots,m\)) is the weight of predictors. \(D_{rt}\) estimates the neighborhood of the prediction value \(X_{r}=\{x_{1n},\)\(x_{2n},\)\(x_{3n},\)\(\ldots,\)\(r\}\) in real-time using former observation value of \(X_{t}=\{x_{1b},\)\(x_{2b},\)\(x_{3b},\)\(\ldots,\)\(x_{mr}\}\). The classification ensemble approach is based on the aggregation of the outputs of a number of the individual classifier by weighted or unweighted averaging [114]. According to the 'no-free-lunch' theory [115; 116], it is assumed that the weaker classifiers with different biases can achieve better performance than the better ones [114; 117; 118].