## 4 Application
### Comparing Results  
First, to evaluate the effectiveness of the proposed feature selection method in tumor region segmentation, especially in distinguishing active tumor regions from necrotic regions, we used K-means cluster analysis. This unsupervised learning method allows us to thoroughly assess the role of features in tumor region segmentation by clustering feature data points into distinct clusters. Through K-means cluster analysis, we divided the tumor region into two clusters: the active tumor region and the necrotic region. Figure 12 presents the visualization results of our method alongside other feature selection techniques. As shown in the figure, the proposed method demonstrates superior accuracy in delineating tumor boundaries and extracting overall image features. Clinically, accurate segmentation of tumor regions--especially in distinguishing active tumor areas from necrotic ones--can significantly aid in treatment planning, such as radiation therapy or surgery, by providing better-targeted intervention. This ability to refine tumor characterization can also help monitor the progression or regression of the tumor, allowing for more informed decision-making regarding patient care. Next, to validate the effectiveness of the proposed feature selection method in preserving intrinsic data structures, we compared the clustering quality of different methods using three internal validation indices: Silhouette Coefficient (SC), Calinski-Harabasz Index (CHI), and Davies-Bouldin Index (DBI). As shown in Table 5, the proposed method achieved the highest SC (0.41 \(\pm\) 0.02) and CHI (275.8 \(\pm\) 22.5), along with the lowest DBI (1.12 \(\pm\) 0.07), outperforming all baseline and state-of-the-art methods. The proposed method significantly improved cluster compactness and separation compared to the baseline (0.41 vs. 0.21, \(p\) < 0.001, _t_-test), indicating that the selected features better distinguish glioma subtypes. Notably, it surpassed SCFS by 46.4%, suggesting enhanced robustness to noise in PET/CT imaging. For CHI, the higher CHI value (275.8 vs. 268.4 for MCFS) demonstrates a more favorable balance between intra-cluster homogeneity and inter-cluster heterogeneity. This aligns with the biological diversity of glioma phenotypes (e.g., IDH-mutant vs. wild-type) captured by [68]Ga/Pentixafor PET features. For DBI, the lower DBI (1.12 vs. 1.38 for MCFS) implies reduced overlap between clusters, which is critical for precise patient stratification in clinical practice. Figure 12: Visualizations of the suggested method and all compared algorithms on the PET dataset, with k = 200 features selected for each method. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **SC** & **CHI** & **DBI** \\ \hline Baseline & 0.21 \(\pm\) 0.03 & 152.3 \(\pm\) 12.1 & 1.98 \(\pm\) 0.15 \\ SCFS & 0.28 \(\pm\) 0.04 & 198.6 \(\pm\) 15.7 & 1.67 \(\pm\) 0.13 \\ UDFS & 0.30 \(\pm\) 0.03 & 223.1 \(\pm\) 16.9 & 1.53 \(\pm\) 0.09 \\ MCFS & 0.35 \(\pm\) 0.02 & 268.4 \(\pm\) 20.3 & 1.38 \(\pm\) 0.08 \\ DUFS & 0.31 \(\pm\) 0.03 & 234.5 \(\pm\) 17.6 & 1.49 \(\pm\) 0.10 \\ DGA & **0.41 \(\pm\) 0.02** & **275.8 \(\pm\) 22.5** & **1.12 \(\pm\) 0.07** \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Internal clustering validation of feature selection methods on [68]Ga-Pentixafor PET/CT glioma data. (The best outcomes are indicated by bold). Clinically, these results are highly significant as they suggest that our method can identify and preserve key discriminative features that reflect the molecular and phenotypic heterogeneity of gliomas, such as IDH mutation status, which is crucial for prognosis and treatment decisions. By improving tumor subtype classification, our method may facilitate personalized treatment strategies, allowing clinicians to better tailor interventions, including targeted therapies, radiation, and surgical planning.