摘要： 为更有效地分析和处理小样本多元数据,提出了一种基于主元选择的偏最小二乘回归方法,并阐述了该方法的基本原理和计算步骤。该方法首先根据相关系数矩阵选取数据样本中的主元,然后对主元进行主成分分析、典型相关分析和多元线性回归。实例分析表明,与偏最小二乘回归方法相比,该方法在分析存在多重线性相关的小样本多元数据方面回归次数更少,精确度更高。

关键词: 主元选择, 偏最小二乘回归, 小样本多元数据, 多重相关

Abstract: To analyze multivariate data with few observations more efficiently, a new partial least-squares regression method based on principalvariables selection is proposed, and the basic theories and calculation process of the method is explained. The method selects principal variables indata samples by correlative coefficients matrix, and then regresses the principal variables by partial least-squares regression. Compared with partialleast-squares regression method, the method has higher precision and fewer regression steps to eliminate the multicollinearity in data. It is illustratedthat partial least-squares regression method based on principal variables selection is more effective and accurate in analyzing multivariate data withfew observations than partial least-squares regression method.

中图分类号: 

• O241.5