## 4 Results and Discussion  
### Clustering Result of Noise Data Set  
The k-means++ cluster method was adopted to classify a noise dataset into different noise types. As the clustering algorithm is unsupervised learning, there is too much uncertainty for it to attain class labels. To evaluate the performance of the clustering algorithm used in this paper, class labels were assigned for different noise types. In this way, the effect of the clustering algorithm could be evaluated based on the following five indicators:  
* V-measure indicates the harmonic mean of completeness and homogeneity. It is used to express the linear dependency between the cluster number and the sample number;
* Rand Index (RI) is the indicator to evaluate the similarity of two clusters;
* Adjusted Rand Index (ARI) is the improved version of RI, which is used to eliminate the influences of random label on RI;
* Normalized Mutual Information (NMI) is the normalized evaluation indicator to quantify the similarity between two clusters;
* Adjust Mutual Information (AMI) reflects the correlation between the cluster label and the ground truth label. It can be used for the consistency test of the clustering algorithm.  
The values of five clustering evaluation indicators fall within the range of 0 to 1. Better performing clustering algorithms have larger indicator values.  
This paper mainly studies the influence of noise data sampling length and decomposed IMF numbers on clustering performance. As shown by Figure 8a, the optimal noise sampling length is 512 from the perspective of noise clustering performance and computation. Before using the clustering algorithm to classify different types of noise, the raw noise data set was processed with VMD. A key factor affecting VMD feature extraction is the numbers of decomposed IMF. The clustering evaluation indicator values and computation times for different numbers of decomposed IMF are shown as Figure 8b. As shown in this figure, the optimal number of IMF was 6.  
Figure 9 shows the superiority of the noise clustering algorithm based on the combination of VMD algorithm, PCA and K-means++; four groups of clustering results were determined as follows:  
* (a) K-means++ for raw noise data: the k-means++ algorithm was directly performed on the raw noise dataset;
* (b) K-means++ for raw noise data with PCA: clustering analysis was performed with K-means++ algorithm for the noise data after PCA dimension reduction;
* (c) K-means++ for raw noise data with VMD: clustering analysis was performed with K-means++ algorithm for noise data after VMD feature extraction;
* (d) K-means++ for raw noise data with VMD/PCA: features of original noise data were extracted with VMD and PCA first and the clustering analysis was performed with K-means++.  
Figure 8: The influence of noise data sampling length and number of IMF on clustering performance.  
As shown in Figure 9a, the result of noise classification clustering with raw data directly was not ideal. In comparison, as shown by Figure 9b, the clustering result was clearly improved when the noise data were initially processed with PCA dimension reduction. As shown by Figure 9c, the clustering result could also be improved significantly if noise classification clustering is performed after VMD noise feature extraction. Finally, the clustering algorithm based on the combination of VMD and PCA dimension reduction method delivers good performance in noise classification.