Numerical Simulation and Optimization of Grey Relational Analysis Models for Panel Data

The indicators-coupled grey relational analysis (ICGRA) models are important in clustering panel data with cross-sectional dependence. However, there is still little research on performance validation for the various ICGRA models. In this paper, we investigate the performance of the existing ICGRA models accounting for the reordering of indicators. Firstly, the robot execution failures (REF) dataset of the University of California Irvine (UCI) machine learning database is adopted to validate the robustness of four traditional ICGRA models. Then, we compared the grey relational orders for all arrangements of indicators in panel data. Simulation experiments showed that the four ICGRA models are not all robust against the grey relational order. To resolve this problem, we adopted the mean value theory and deep modeling to optimize the four models and compared them with the tetrahedral grey relational analysis (GRA) model that considers the coupling effect between indicators on the grey relational order, as well as with the k-nearest neighbor (KNN) algorithm. Results show that the classification accuracy of the averaged absolute GRA model was 97.73%, the other optimized ICGRA models and the k-nearest neighbor (KNN) method all achieved 100% accuracy, while the tetrahedral GRA model has an accuracy of 83.33%. Therefore, the average grey incidence degree for all arrangements of indicators and deep modeling significantly improves the stability of models and enhances the clustering accuracy in different cases.OPEN ACCESS Received: 09/12/2024 Accepted: 04/03/2025 Published: 30/06/2025