## 1 Introduction  
With the rapid advancement of society and the advent of the big data era, both the volume and dimensionality of data have increased exponentially, resulting in a growing demand for efficient data processing and analysis. High-dimensional data, which are widely encountered in fields such as biometrics, computer vision, and medical imaging, provide rich information but also introduce substantial noise and redundancy, making data analysis more challenging. As dimensionality increases, data distribution becomes sparser, the search space expands, computational complexity rises, and the generalization ability of models tends to decline. Feature selection offers an effective solution by identifying a representative subset of features from the original dataset, which not only improves feature quality and reduces computational cost but also mitigates the curse of dimensionality and enhances model performance, all while preserving the intrinsic structure of the data. Feature selection methods can be divided into supervised [1; 2], semi-supervised [3; 4], and unsupervised [5] approaches depending on whether the data labels are fully available, partially available, or entirely unavailable. In many real-world applications, labels are often difficult or impossible to obtain, which limits the applicability of supervised and semi-supervised methods. As a result, unsupervised feature selection, which relies on the intrinsic structure of high-dimensional data rather than label information, has gained increasing attention and demonstrated notable advantages in handling unlabeled data effectively. According to different selection strategies, feature selection methods can be classified into filter, wrapper, and embedded approaches. Filter methods evaluate feature quality using statistical criteria such as information distance, task relevance, and redundancy and select features based on corresponding scores, with typical algorithms including the Laplacian Score [2], maximum variance, trace ratio, and SPEC [3]. These methods are computationally efficient, model-independent, and highly generalizable; however, they often fail to adapt well to specific tasks or datasets [6]. In contrast, wrapper methods, such as varFnMS [7] and UFSACO [8], perform feature selection based on the predictive performance of selected feature subsets using a specific learning model. While they generally achieve better performance than filter methods, their computational cost is significantly higher, particularly for large-scale datasets, due to the need for repeated feature subset searching and evaluation. Embedded methods integrate feature selection directly into the model training process, enabling the simultaneous optimization of feature subsets and learning models. This approach typically offers improved efficiency over wrapper methods and better task-specific adaptation than filter methods. In this study, we focus on embedded unsupervised feature selection methods, which can generally be divided into regression-based and self-representation-based frameworks. The self-representation-based approach assumes that each feature can be reconstructed as a linear combination of related features. For example, [PERSON] et al. [9] proposed UFS_SP, and [PERSON] et al. [10] introduced NLRL-LE, which employs non-convex constraints and Laplacian embedding for latent representation learning. Similarly, [PERSON] et al. [11] developed MFFS, a method based on matrix factorization that selects a subset of features capable of representing the remaining features via subspace learning. On the other hand, regression-based methods convert the unsupervised selection problem into a supervised paradigm by generating pseudo-labels for the dataset. For instance, SCFS, proposed by [PERSON] et al. [12], utilizes symmetric non-negative matrix factorization to derive a cluster indicator matrix, then applies regression to optimize the coefficient matrix and identify the most informative features.