## 3 Data Analysis Setup
### Feature Space Extension  
Due to the stochastic and probabilistic nature of wave-governing parameters such as height and period, the feature space must be spacious; in this context, a sub-optimal trained model especially concerned with computational efficiency. As the number of inputs increases, neural networks encounter k\({}^{4}\) order overparameterization. However, prioritizing the model's ability to accommodate massive inputs is essential. Thus, it is significant to assess whether the ML model can effectively handle the data with both computational efficiency and accuracy.  
To address the first issue, two parameters can be worked out in the current data analysis setup: first, the range of features for each pixel equivalent to the local normalization of the wavelet coefficient; and second, the reorganization of features of matrix K to the n number of vectors projecting on more planes based on the wavelet intensity. Reorganizing features allows directly relating the particular response to the wave parameters label with two features. These features in the form of vectors for any specific time segment hold two values between 0 and 0.5 and 0.5 and 1 according to Equation (9) that represent endogenous characters, which can be further statistically worked out as the new attributes for the input-output relationship. Feature engineering on new features also enhances the entropy for the newly added attributes that can assist in better classification. This issue has been extensively explained in Section 4, where the uniqueness impacts feature classification considerably. In Equation (9), this can be characterized by Y which has been set to 255 for initial test. However, the extension of this value dictates the uniqueness of features and correspondingly the permutations to the wave parameters that is indirectly linked to computational resources. Figure 10 indicates the extension of Y and corresponding number of unique permutations that can be achieved for features. Simply, for 2056, the number of particular features is of the order of N\({}^{2}\) equals to 4,227,136 numbers of unique permutations of features.  
On the other hand, increasing the number of projections plane adds two more possibilities. First, it amplifies the number of distinct permutations between vectors taken from each plane while preserving feature uniqueness in each vector. Second, due to uniqueness, the newly engineered attribute will show high variance that improves the classification. All these concepts will be practically demonstrated in Section 4. The immediate result is a notable extension in the range of scenarios targeted for modeling waves, whether using these approaches separately or in combination. Figure 10 also indicates increasing the number of permutations based on the projection plane that grows exp  
Figure 10: Increasing the number of features through normalization (**a**) and increasing the number of features via projection plane (**b**).  
it must be noted that despite feature space extension, increasing projection planes incurs computational costs for further training, so a trade-off seems to be necessary.  
In summary, the proposed data analysis process enables the extraction of detailed features from the system's response to external forces, combined with the system's characteristics, which can be labeled by the user (supervised ML) with the corresponding wave parameters. Additionally, the current mechanism shrinks the detailed stochastic features to the unique normalized values representative of each deterministic scenario. This setup not only reduces the computational costs due to the compression of fine features and their unique representation but supports the extensive number of unique features. The proposed mechanism shares similarities with the encoder in a variational autoencoder up to the latent space. However, it incurs lower computational cost since it is less mathematically intensive and does not rely on operations involving neurons and nodes.