## 5 Discussion  
In this paper, we propose a novel unsupervised feature selection method based on a DGA, which integrates dual-graph regularization and a norm-based sparsity constraint into an autoencoder framework. This design allows DGA to effectively capture the intrinsic local geometric structures of both data and feature spaces while enhancing robustness against noise and outliers in high-dimensional data. From a clinical perspective, the results obtained on [68]Ga-Pentixarof PET/CT imaging data from glioma patients are particularly encouraging. The selected features--especially those reflecting CXCR4-mediated metabolic activity--demonstrated meaningful alignment with known molecular markers such as IDH mutation status and CXCR4 receptor expression. By achieving a Silhouette Coefficient of 0.41 and a Calinski-Harabasz Index of 275.8, DGA significantly outperformed baseline methods, suggesting its potential utility as a non-invasive tool for tumor subtyping and prognostic stratification. In clinical practice, this could aid in treatment decision-making and improve patient outcomes by tailoring therapies to the biological behavior of individual tumors. However, the current analysis is based on a dataset containing only 24 glioma patients, which may limit the generalizability of the conclusions. To strengthen statistical power and clinical applicability, future studies will include larger patient cohorts, preferably from multiple centers, to ensure robustness across diverse clinical scenarios. Despite these strengths, DGA is not necessarily the endpoint. The current optimization procedure--based on gradient descent--faces challenges due to the non-convex and non-Lipschitz nature of the objective function, which may result in convergence to local optima. To address this, future work could explore global optimization strategies such as evolutionary algorithms, continuation methods, or stochastic annealing to improve convergence reliability. Moreover, while the current model uses a fixed activation function and architecture, future improvements could involve adaptive or learnable activation functions, which may better accommodate multimodal data distributions, especially when integrating PET with MRI or genomic data. Introducing attention mechanisms or graph neural networks (GNNs) could also enhance the model's ability to focus on clinically relevant features. Lastly, the incorporation of genomic biomarkers such as MGMT methylation or 1p/19q co-deletion status could further enhance the model's clinical value, enabling its integration into precision oncology workflows. Conceptualization, Z.S. and M.C. ; methodology, Z.S. and M.C. ; software, Z.S. and M.C. ; validation, X.F. and L.X. ; formal analysis, Z.S., M.C., X.F., and L.X. ; investigation, X.F. and L.X. ; writing--original draft preparation, Z.S. and M.C. ; writing--review and editing, X.F. and L.X. ; visualization, X.F. and L.X. All authors have read and agreed to the published version of the manuscript. This research is supported by the Fundamental Research Funds for the Central Universities (Grant No. 104972024 KFYjc0063). **Institutional Review Board Statement:** The [\({}^{68}\)Ga]Ga-Pentixarof PET/CT glioma dataset used in this study is publicly available and was collected in accordance with ethical standards as described in the original publication [37]. No new patient data were collected or used in this research. **Informed Consent Statement:** The glioma PET/CT data used in this study were obtained from a publicly available and anonymized dataset. All data collection procedures were conducted by the original investigators in compliance with relevant ethical standards. No additional data collection from human participants was conducted by the authors of this study. **Data Availability Statement:** The glioma PET/CT data used in this study are publicly available and can be accessed at [37].