## 1 Introduction
In summary, most existing unsupervised feature selection methods primarily emphasize the structural information of the data space while largely neglecting the structural properties of the feature space. Additionally, effectively eliminating noise from high-dimensional data remains a significant challenge. To tackle these issues, we propose an unsupervised feature selection approach based on a dual-graph autoencoder (DGA), the framework of which is illustrated in Figure 1. The proposed DGA framework employs an autoencoder structure that reconstructs data through encoding and decoding processes, with feature importance determined by the encoder's weight matrix. To enhance robustness and sparsity, we apply \(\ell_{2,1/2}\)-norm regularization to both the encoder weights and loss function while using \(\ell_{2,1}\)-norm for the decoder weights. The framework preserves data structure by maintaining the manifold structures of both data and features during reconstruction. Finally, clustering experiments are conducted on the selected feature subset to evaluate performance. This algorithm improves the performance from two aspects: (1) it increases the flexibility of data space reconstruction, and (2) it simultaneously preserves both data structure and feature structure during the reconstruction process. By integrating an autoencoder with dual-graph regularization, the model not only improves the accuracy of reconstruction but also retains essential feature information. Moreover, the incorporation of a norm constraint helps to suppress the influence of noise and outliers. The main contributions of this study are summarized as follows:  
(1) We embed dual-graph regularization into the autoencoder to preserve the manifold structures of both the data space and feature space during the reconstruction process. (2) To promote sparsity and reduce feature redundancy, we impose \(\ell_{2,1/2}\)-norm and \(\ell_{2,1}\)-norm constraints on the weight matrices of the encoder and decoder, respectively, thereby enhancing the effectiveness of feature selection. (3) To boost the robustness of the algorithm against noise and outliers present in real-world data, the \(\ell_{2,1/2}\)-norm is introduced into the autoencoder's loss function. (4) We apply the proposed method to the publicly available [\({}^{68}\)Ga]Ga-Pentixafor PET/CT images of glioma patients, performing unsupervised feature selection on PET scans. The results demonstrate the potential of our approach to assist in the diagnosis and analysis of gliomas by identifying discriminative features that characterize tumor regions. The structure of the remainder of this paper is organized as follows. Section 2 reviews related work and presents the proposed method in detail, including the corresponding optimization strategies. Section 3 evaluates the performance of the proposed DGA by comparing it with several existing methods on nine benchmark datasets. Section 4 further demonstrates the effectiveness of the proposed method using the [\({}^{68}\)Ga]Ga-Pentixafor PET/CT glioma dataset in an unsupervised clustering task. Finally, Section 5 concludes the paper with a summary of the key findings and potential directions for future research.