## 1 Introduction  
Feature selection is an important task for the high-dimensional low-sample-size (HDLSS) datasets that are prevalent across various domains, such as text recognition, finance, and gene expression microarrays. HDLSS datasets are characterized by many features relative to the limited number of available samples. For instance, in microarray datasets, the number of features (representing genes) is often greater than thousands, whereas the sample size remains small [1]. An HDLSS dataset requires a reduction in the dimensions of the feature space. Reducing dimensionality not only decreases model complexity but also improves model prediction accuracy [2]. In the context of HDLSS datasets, a predominant challenge emerges: a significant number of features do not contribute to the accurate prediction of the target variable. However, these features can be irrelevant or redundant. Therefore, the principal objective of managing HDLSS datasets is to select and rank features that offer substantial insight into the desired outcome, ensuring that the model's predictive capacity is optimized. The analysis of microarray gene expression datasets has gained significant attention in the fields of data mining and machine learning [3]. As scientists strive to identify key features within HDLSS datasets, diverse feature selection methods have been proposed and categorized into filter, wrapper, hybrid, and embedded methods. In microarray datasets that include thousands of features, many features are correlated because they originate from the same source. Correlated features tend to form clusters that collectively affect the outcomes [4], suggesting that selecting groups of correlated features is more effective than selecting individual features. This approach is known as group feature selection and recognizes the interdependence of each cluster. Group feature selection methods aim to discard irrelevant and redundant group features that cause a decrease in classification accuracy, while retaining only informative group features, thereby enhancing the computational efficiency and classification performance [5]. [PERSON] [6] introduced the probing least absolute square modeling (PLASM) method for group feature selection, extending the principles of the least absolute shrinkage and selection operator (lasso) method [7] to the group level. [PERSON] and [PERSON] [8] further advanced [PERSON]'s PLASM method, pioneering the development of a group lasso for group feature selection (GFS), which was a significant breakthrough in this domain. [PERSON] et al. [9] extended the group lasso method to logistic regression and applied it specifically to DNA sequence data. Additionally, [PERSON] et al. [10] proposed the sparse-group lasso method, introducing sparsity considerations at both the within-group and group levels. [PERSON] et al. [11] took this a step further by developing an adaptive sparse-group lasso. [PERSON] and [PERSON] [12] proposed a multinomial sparse-group lasso as an extension of the sparse-group lasso. Group lasso and its extensions are very effective gene selection and classification methods for microarray datasets. Many studies have applied the group least squares (GLS) method for group feature selection. In the group lasso penalty, features are considered in a group manner [5; 13]. Despite these advancements, existing group feature selection methods have inherent limitations, in that they fail to quantify the relative importance of the selected group features. These methods can identify some feature groups as relevant but do not distinguish those that are most relevant to a target variable. [PERSON] and [PERSON] [14] proposed a group feature (GF) ranking and selection approach that is applicable only to binary-class datasets. Consequently, the existing methods cannot determine the relative importance of group features for multiclass datasets. Thus, the existing methods cannot provide insight into how selected groups contribute compared to others, thereby limiting the interpretability of the model.