关键词: 指标筛选, 多维关联, 主成分分析, 因子分析, 灰色关联分析

Abstract:

In view of the challenges such as multi-dimensional correlations, multi-collinearity, data scarcity, and irregularity faced in the indicator screening of combat capability assessment, a simple and reliable screening method that combines qualitative and quantitative is proposed. Firstly, principal component analysis (PCA) and factor analysis (FA) are used to reduce the dimensionality of the indicators. Redundant information is eliminated from the perspectives of covariance matrix decomposition and latent factor extraction respectively. Secondly, combining expert experience and correlation analysis, the preliminary screening results are qualitatively optimized to ensure they meet the actual combat requirements. Finally, grey relational analysis (GRA) is introduced to quantify the dynamic correlation strength between the reduced-dimensionality indicators and combat capabilities, enhancing the adaptability of the method to small samples and irregular data. PCA/FA addresses the problem of data redundancy, and GRA makes up for the insufficient adaptability to small samples. The three methods form a screening framework of “dimensionality reduction-reconstruction-correlation”. Simulation results demonstrate that the proposed method effectively eliminates multi-collinearity among indicators and streamlines the indicator system. Even in scenarios involving small samples and irregular data, it reliably identifies core indicators highly correlated with combat capability, thereby validating the method’s feasibility and validity.

Key words: indicator selection, multi-dimensional correlation, principal component analysis (PCA), factor analysis, grey relational analysis (GRA)