# Application of Machine Learning Tools for Long-Term Diagnostic Feature Data Segmentation
## 5 Simulated Data Analysis
### Extraction of Features for Simulated Signal for Gaussian Noise Case  
In Figure 7, seven initially extracted features for Gaussian noise case are plotted.  
Based on visual inspection of each statistical feature, three features are selected for further processing, namely STD, RMS, and mean value. They are selected because their shapes are the most similar to the original curve. In Figure 8, a 3D plot of these three features is presented. One may notice that three potential clusters are possible. In the Figure 8 3D plot, one can notice internal dependence/correlation in the data, thus a PCA is applied. Indeed, as one can see in Figure 9, PC1 contains nearly 100 % information. In Figure 10, a comparison of three original features and PC1-PC3 features are presented. One may see a strong correlation between the original features and PC1.  
Figure 6: Input simulated data for non-Gaussian \(\alpha-\)stable noise with \(\alpha=1.8\). (**a**) deterministic component, (**b**) random component, (**c**) simulation of the signal  
Figure 7: Statistical features for simulation signal in presence of Gaussian noise.  
As mentioned above, as original features are highly correlated and the PC1 contains most of the information, the clustering can be done simply. In Figure 11, one can see the trajectory of PC1 (left) and its probability density function. One can easily notice that the clustering can be done simply by the Gaussian noise.  
Figure 8: Features space for simulation signal in presence of Gaussian noise.  
Figure 10: PCA of raw features for simulation signal in presence of Gaussian noise.  
Figure 9: PCA score for simulation signal in presence of Gaussian noise.  
three modes related to three regimes: the first one with amplitude less than 0 is related to regime (good condition), second one with amplitude more than 0 and less than 10 (warning condition) and samples with amplitude above 10 could be considered as regime 3. In Figure 12, the result of clustering in PC1-PC2 space is presented. The degradation development goes from the left side (green cluster) through points cloud in yellow color to several point constituting \"Alarm\" cluster. As one can see EM, BIRCH and K-means detected three classes with different results. For example, the EM algorithm detected the first and second regimes earlier than other approaches, while K-means and BIRCH discovered the last regime the same. However, the result for the second regime is different. Moreover, BIRCH and K-means recognized more (than EM) points as \"Good Condition\", i.e., they may have some trouble recognizing the border between class 1 and class 2 (good and warning) properly.  
Figure 11: PC1 time series, its kernel density of PC 1 and final segmentation results for simulation signal in presence of Gaussian noise.  
Figure 12: The output of clustering algorithms for simulation signal in presence of Gaussian noise: (**a**) EM result, (**b**) K-Means Result, (**c**) BIRCH result.  
Finally, in Figure 13, the results of segmentation based on selected clustering algorithm are presented. In Figure 13, one may find a confirmation that K-means and BIRCH recognized too many points as a \"good condition\" cluster. The change point between the good and warning segment is much later than for the EM algorithm. Hence, one may conclude that the EM algorithm is the best solution here. The exact values of changing point (CP) are presented in Table 2.