## 3 Data Analysis Setup
### Inspiration and General Framework  
As discussed, the very shortcoming with the conventional approaches thus far has been the feature engineering before feeding data into the ML network. Ideally, to perform the effective input/output mapping, the association of details in the form of attributes to each batch of data increases the entropy and eventually enhances the separability. However, the challenge arises from the multitude of scenarios and the overlap of features among various attributes. Consequently, a significant amount of data is necessary to improve the distinction between nearly identical features while maintaining information entropy as given by Equation (5), where p: \(\mathbb{X}\) belong to probability between 0 and 1, X is a discrete random variable (RV), and p(x) is probability distribution. As broadly discussed in seminal work [7], higher entropy amounts to higher information tantamount to more possible state of outcomes which positively helps in the separation of features between different classes in certain conditions. \[\mathrm{H(X)}=-\sum_{\alpha\in\mathbb{X}}\mathrm{p(x)logp(x)} \tag{5}\]  
The repercussion is computational deficiency since many neurons are required to not only distinguish these differences for pattern recognition but also to be trained by nuanced features. However, by encoding (compressing) the detailed attributes before uniquely mapping each scenario, the computational cost can be substantially reduced. The challenge arises when extensive features exist in the departure domain, requiring association with categorical labels during mapping. This issue becomes more challenging for deterministic purposes for two reasons. First, the observation window is small, so it is hard to provide feature uniqueness concerning class labels. Secondly, overall extension of features is vast, resulting in a large spread between various observations of the same class. However, it is easier to link the attributes by spreading commonality as a thread for longer observation lengths, where the statistical properties come into the picture. The present feature engineering has been designed to address the above two discussed issues. However, it can serve other purposes, i.e., Part A [7]. The general process of the current approach is outlined in the flow diagram depicted in Figure 6. The first outcome, focusing on feature manipulation, was discussed in the previous issue. This issue aims to delve into the second outcome, which concerns feature classification. Figure 6: Data analysis flow diagram. Beginning from the left side of the diagram, the wave, acting as the input, excites the floating object, functioning as the system, resulting in 6 DOF responses presented as time series as the system output. The objective of employing wavelet analysis on short segments of these time series is to extract maximal information from the data. Subsequently, these features undergo numerical rearrangement, facilitating eventual manipulation and classification based on the wave class. The final grey blocks denote the outcomes of feature engineering, providing direct control over the refined features. The first outcome was discussed in Part A, and the current setup aims to delineate how it leads to the training cost reduction. In the following, the mathematical description is delineated. The representation of the 6 DOFs must adhere to a specific format to enable further mathematical operations. At this stage, the time series is initially segmented into small observation windows of \(\left\{\mathrm{y}(\mathrm{k})_{\mathrm{ij}}\,\mathrm{y}(\mathrm{k})_{\mathrm{ ij}},\ldots\,\mathrm{y}(\mathrm{k})_{\mathrm{Nj}}\right\}\) for i = 1:N, 40 s for current purposes and j = 1:6 denotes DOFs. Subsequently, each individual DOF, or the linear combination of time series forms a new time series, as is the approach adopted here. Despite encompassing all numeric features within the data, this new time series does not carry any inherent physical meaning [15].