# A Quantitative Evaluation of UAV Flight Parameters for SfM-Based 3D Reconstruction of Buildings
## 4 Validation
### Single Shooting Pattern
#### 4.1.4 Principal Component Analysis and K-Means Clustering  
To mitigate the complexity of the multidimensional performance space composed of multiple disparate SfM result metrics and effectively identify the intrinsic structure of the data, we sequentially applied principal component analysis (PCA) and k-means clustering techniques. First, PCA was used to reduce the multivariate performance data into a smaller set of core principal components (PCs), making visualization and interpretation easier. Subsequently, the k-means clustering algorithm was applied to group shooting settings (data points) with similar performance characteristics, aiming to classify overall performance patterns and identify the unique characteristics of each cluster. To ensure the robustness of the analysis, rows containing outliers defined based on missing values and the interquartile range (IQR) were preemptively removed from the original data before performing PCA and clustering (Table 7).  
For the analysis, we standardized six key performance metrics (Reprojection Error, Final Points, Mean Track Length, Point Density, Computation Time, Reconstruction Completeness) and then performed PCA. The results showed that the top three principal components (PC1, PC2, PC3) explained approximately 82.8% of the total data variance (individual explanatory power: PC1 43.5%, PC2 22.6%, PC3 16.8%). This indicates that a relatively small number of principal components effectively summarize a significant portion of the information in the original data without loss, successfully achieving dimension reduction.  
PCA is useful for interpreting complex multivariate data, and by analyzing the correlations (loading values) between each principal component axis and the original variables, one can understand their meaning. For example, if the loading value analysis shows that PC1 has a high positive correlation with indicators related to 'overall reconstruction quality and detail' and a negative correlation with Reprojection Error, then the PC1 axis can be interpreted as a comprehensive indicator of model quality. Similarly, PC2 may show a high correlation with variables related to 'computational efficiency'. Next, we applied the Elbow method to determine the optimal number of clusters (k) for cluster analysis. By observing  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Principal Component** & \
\begin{tabular}{c} **Individual Explained** \\ **Variance (\%)** \\ \end{tabular} &
\begin{tabular}{c} **Cumulative Explained** \\ **Variance (\%)** \\ \end{tabular} \\ \hline PC1 & 43.5 & 43.5 \\ PC2 & 22.6 & 66.1 \\ PC3 & 16.8 & \(\approx\)82.8 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Explanation of top principal components.  
the changes in the within-cluster sum of squares, the 'elbow' point where the slope of the graph curve becomes the most gradual was clearly identified when the number of clusters was 2, and the optimal number of clusters was finally determined to be 2.  
Using the determined optimal number of clusters (k = 2), k-means clustering was performed, and the results were visualized in a two-dimensional space with PC1 and PC2 as axes (Figure 4). The visualization results showed that the two clusters (Cluster 0 and Cluster 1) tended to be relatively clearly distinguished based on the PC1 axis. Specifically, Cluster 0 was mainly distributed in the negative region of PC1, while Cluster 1 was primarily located in the positive region of PC1. However, some data points were observed to be mixed in the boundary region between the two clusters.  
In conclusion, the unsupervised learning analysis combining PCA and k-means clustering strongly suggests that the extensive UAV-SfM shooting settings tested in this study do not simply form a continuous performance spectrum but naturally divide into two distinct performance profile groups when considering multiple performance metrics comprehensively.