## 4 Experimental Results and Discussion
### Feature Selection Analysis  
The Fisher score with permutation entropy, which is described in Section 3.3, is utilized to filter redundant features as a feature heuristic selection method. Specifically, the embedded dimension parameter of permutation entropy is set to 6. Based on the experimental trial, the time delay parameter of permutation entropy is set to 1. The hard threshold of permutation entropy is set to 0.6. Figure 9  
Figure 8: PGD signal decomposition results by WPD. (**a**) When the decomposition level is 2 by WPD; and, (**b**) when the decomposition level is 3 by WPD. Figure 7: Power quality disturbances (PQD) signal decomposition results by variational mode decomposition (VMD). (**a**) When K = 3 by VMD; (**b**) when K = 4 by VMD; (**c**) when K = 5 by VMD; and, (**d**) when K = 6 by VMD. presents the correlation of the top 16 selected features, which represent the IMF2 RMS, IMF2 standard deviation, IMF2 variance, IMF2 average deviation, IMF2 kurtosis, IMF2 skewness, IMF2 range, IMF2 permutation entropy, IMF1 permutation entropy, IMF1 variance, IMF1 standard deviation, IMF1 RMS, IMF1 average deviation, IMF1 kurtosis, IMF1 range, and IMF4 permutation entropy. As shown, each feature is imported into the training dataset to determine the classification accuracy, with the aim of showing the effectiveness of the feature selection method. The experiments are conducted 50 times to avoid errors and stochastic disturbances. Subsequently, the accuracy results are generated by averaging the calculations. If the feature is irrelevant to the target class, the corresponding Fisher's score is nearly zero. Hence, the average accuracy of the classification would be poor. Conversely, if the feature is highly relevant, the corresponding Fisher score is relatively large. Thus, the classifier that is constructed by relevant features would achieve perfect accuracy. Moreover, the threshold value of the selected feature is very important. Threshold selection is discussed in the following paragraph. In this case, the SVM classifier is adopted to focus on the effects of the selected features. To be specific, the sample data sets are partitioned into 10 equal folds, and the tests were performed in 10 iterations. The number of each test instance is 1000. For the SVM classifier, the cost values C and \(\gamma\) of the SVM model are set to 100 and 0.02, respectively, and the linear kernel is selected as the kernel function. The classification threshold is set to 0.5. For each PQD class, the data sets were split into the training data sets and the test data sets. The ratio of the samples for the training and test is 4:1. Two feature ranking methods, [PERSON]'s score only and [PERSON]'s score with the permutation algorithm, were used for feature selection for comparison. Figure 10a,b show the precision and recalls results by extracting different features according to the [PERSON]'s score only and [PERSON]'s score with the permutation algorithm, respectively. The average precision and average recall ratio reached 96.5% when the top 24 ranked features were selected by the [PERSON]'s scoring algorithm. Similarly, the average precision and the average recall ratio according to the [PERSON]'s score with the permutation algorithm achieved 97.6% when the SVM classifier was trained by feeding the 16 top-ranked features. However, the SVM classifier that was trained by the [PERSON]'s score with the permutation selection algorithm showed better performance. Moreover, it cost less dimensions for feature vectors. Interestingly, as observed from the average precision and the average recall ratio, the accuracy was initially increased with the increased number of top-ranked features, because the decision boundary of the SVM hyperplane is more clearly separated by increasing the relevant feature vectors. However, once the feature dimension reached the proper ranking feature point, the performance of the classifier continued to decrease due to redundant features.