## 4 Data Analysis Framework Application
### Model Training  
For training purposes, various ML and DL networks can be utilized, e.g., regression and classification models. To this end, the input-output data from the experiment can be directly used for classification or training the regression model. However, as elaborated in Part A, the computational issues arise for both techniques; for classification, the given importance to meticulous nonlinear behaviors that carry the detailed behavior of the system is as much as the governing characteristics and lower order terms. This can end up with unnecessary costs for higher order terms on the one hand, and on the other hand, the network allocates the same importance for both intrinsic behaviors of the system. On the other hand, the low variance of features demands a higher number of neurons for training to capture the detailed nuances. In terms of the regression model, the issue is due to high dimensional space which could be effective if features exhibit variance, helping to construct the regressor. Two approaches can be sought to tackle this. The first is to reduce data features or to apply a low-pass filter to preserve the main characters and construct the regression on this. The second is to reduce feature space through feature reduction techniques such as Principal Component Analysis (PCA). Both methods somewhat overlook the nuanced properties of data essential for characterizing short observation lengths.  
As a result, the current approach is to compress features instead of eliminating features, while transforming the data into a lower dimensional feature space. These operations substantially reduce computational costs for training. To demonstrate, we initially utilized Support Vector Regression (SVR) on the data for regression purposes and compared it with other models.  
SVR, derived from the support vector machine (SVM), is a nonlinear estimation model designed to transform nonlinear data into a high-dimensional feature space. In this space, linear techniques can be effectively applied by identifying an optimal hyperplane. For more detailed information, one can refer to [29]. To evaluate the current data analysis framework,  
Figure 15: Enhancement of features variance using two new additional features.  
the SVR is constructed on data in Table 3 with different batch sizes for max pooling ranging from \(2^{n}\) for n = 3:8, equivalent to 8 \(\times\) 8 to 256 \(\times\) 256 pixels. Also, the number of additional features has been scaled accordingly.  
Two metrics are of importance to measure training time and validation error. For evaluating validation error, the error is computed based on the ratio of incorrectly detected labels. For training, the data was randomly partitioned to an 80/20 ratio initially and then taken through the training process. Figure 16 indicates the obtained validation error versus training time. Evidently, max-pooling size and training time show an inverse correlation. More accurately, for the simplest case of resolution 8, the array of data for training is composed of 14,160 rows and 10 columns for six classes of wave data, where every 10 features are attributed to one class. To examine the effectiveness of data projection feature engineering, both the raw data and the white pixel data were trained using the same setup for a resolution of eight features. The error obtained for the raw data was 36.44%, while the error for the white projection was found to be 83.33%. The results again pronounce the significance of the proposed model to sieve salient features with higher entropy.