## 4 Data Analysis Framework Application
### Projection into More Planes  
Considering all the results obtained thus far, it appears that the data spread can be categorized into three main areas for projection: the black projection plane below 0.5, the black plane above 0.5, and the white plane, each showing varying sensitivity to parameters. For example, the white plane is more sensitive to resolution changes, whereas the primary improvement in the spread of the black plane, facilitated by the data analysis framework, is concentrated in the region below 0.5. This understanding is derived from the monitoring and observability of the new feature space, as outlined in the objective of current research. While it is acknowledged that the spread may vary for other floating objects based on parameters such as dimensions and mass distribution, the new approach enables a deeper insight into these features and, more precisely, comparing features for two different objects to the identical wave. Consequently, the focus on features and further enhancement operations can be adjusted or directed towards specific spectral-amplitude spreads of data.  
That being said, expanding the projection into more planes offers additional advantages for classification and clustering. Technically, it increases the number of unique permutations of features that can characterize any specific wave class by projected vectors. This numerical order is calculated by \(m^{n}\), where \(m\) represents the vector size and \(n\) denotes the number of projections. In the current case, the number of unique features is 65,536. However, the addition of just one more plane increases the number of unique permutations to 16,777,216. As such, incorporating additional projection planes can significantly enhance  
\begin{table}
\begin{tabular}{c c c c} \hline
**Scenario 2 and 3** & **32** & **256** & **Difference (\%)** \\ \hline Exp and Sim total & 0.0325 & 0.0277 & 15.9 \\ Exp and new feature total & 0.0213 & 0.0177 & 18 \\ Change (RMSE) \% & **41** & **44** & \\ Exp and Simulation Black Plane & 0.0300 & 0.0271 & 10 \\ Exp and new feature Black Plane & 0.0209 & 0.0179 & 15.4 \\ Change (RMSE) \% & **35** & **40** & \\ Exp and Sim White Plane & 0.0730 & 0.0020 & 189 \\ Exp and new feature White Plane & 0.0310 & 0.0015 & 181 \\ Change (RMSE) \% & **80** & **28** & \\ \hline \end{tabular}
\end{table}
Table 6: Quantitative outcomes of scenarios 2 and 3.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Scenario 1 and 3** & **32** & **256** & **Difference (\%)** \\ \hline Exp and Sim total & 0.0325 & 0.0277 & 15.9 \\ Exp and new feature total & 0.0313 & 0.0280 & 11 \\ Change (RMSE) \% & **37** & **1** & \\ Exp and Sim Black Plane & 0.0300 & 0.0271 & 10 \\ Exp and new feature Black Plane & 0.0303 & 0.0279 & 8 \\ Change (RMSE) \% & 1 & **2.9** & \\ Expand Sim White Plane & 0.0073 & 0.0020 & 113 \\ Exp and new feature White Plane & 0.0042 & 0.0021 & 66 \\ Change (RMSE) \% & **53** & **4** & \\ \hline \end{tabular}
\end{table}
Table 7: Quantitative outcomes of scenarios 1 and 3.  
the potential capability of feature stratification and improve classification accuracy. Further in-depth discussions on this topic will be presented in part B of the current issue.