基于趋势性改进的灰色主成分聚类模型
Grey Principal Component Clustering Model Based on Trend Improvement

在灰色主成分分析方法的研究中，针对原有方法中用于主成分分析的关联度矩阵的伪相关性和波动型序列量化不准确的问题。在两方面进行改进，一是改进灰色相对关联度的取值范围，将其从0.5~1拓展到0~1；二是基于斜率思路引入了趋势概率关联度指标，度量序列在趋势变化方向上的表征。结合两种关联度，提出了可以替换相关系数或协方差矩阵的新关联度矩阵。模拟与实证结果显示，改进的灰色关联度矩阵能够更好的度量波动型序列特征，将其用于主成分分析聚类，可以发现更加丰富和合理的结果，与一般模型相比效果更优。
In the research of the grey principal component analysis method, the issues of pseudo-correlation and inaccurate quantification of fluctuating sequences in the correlation matrix for principal component analysis were tackled. Two improvements were made in two respects. Firstly, the range of grey relative correlation was expanded from 0.5~1 to 0~1. Secondly, based on the slope concept, a trend probability correlation index was introduced to measure the representation of sequences in the trend change direction. By combining the two correlation indices, a new correlation matrix that can replace the correlation coefficient or covariance matrix was proposed. Simulation and empirical results indicate that the improved grey correlation matrix can better measure the features of fluctuating sequences and be used for principal component analysis clustering to yield more diverse and reasonable results, outperforming general models.