Feature selection, as one of the essential dimensionality reduction techniques, hasbecome one popular yet challenging area in the field, such as data mining andmachine learning. Unlike feature extraction (such as principle component analysis andnon-negative matrix factorization), preserving the entire information but losing thefeature relevance. Data processing in feature selection will lose information, leading tothe need to develop lightweight, efficient, and practical methods that preserve the datainformation as much as possible while performing dimensional reduction. In this paper,we propose a rankability-based feature selection method. The rankability concept wasproposed in 2019, similar to the entropy concept, and has not been studied widely yet.The proposed method is lightweight in terms of complexity, which requires no iterativeoptimization or auxiliary estimator tools.We experimented with sixteen datasets and compared our results with four otheralgorithms. The results show that our rankability-based feature selection methodoutperforms the fuzzy entropy-based method on five datasets in eight, and the averageaccuracy increased by 0.1482, 0.1078, and 0.1157, respectively. Then, in the varieddimension-reducing experiments, the proposed method shows superiority on fourdatasets out of eight and is competitive with others on two datasets out of eight.

Transformer architectures have been applied to graph-specific data such as protein structure and shopper lists, and they perform accurately on graph/node classification and prediction tasks. Researchers have proved that the attention matrix in Transformers has low-rank properties, and the self-attention plays a scoring role in the aggregation function of the Transformers. However, it can not solve the issues such as heterophily and over-smoothing. The low-rank properties and the limitations of Transformers inspire this work to propose a Global Representation (GR) based attention mechanism to alleviate the two heterophily and over-smoothing issues. First, this GR-based model integrates geometric information of the nodes of interest that conveys the structural properties of the graph. Unlike a typical Transformer where a node feature forms a Key, we propose to use GR to construct the Key, which discovers the relation between the nodes and the structural representation of the graph. Next, we present various compositions of GR emanating from nodes of interest and α-hop neighbors. Then, we explore this attention property with an extensive experimental test to assess the performance and the possible direction of improvements for future works. Additionally, we provide mathematical proof showing the efficient feature update in our proposed method. Finally, we verify and validate the performance of the model on eight benchmark datasets that show the effectiveness of the proposed method.