用DEA优化偏最小二乘回归建模及应用

摘要

偏最小二乘回归(PLSR)统计建模方法本质上是对数据平均趋势的估算,无法避免“依据错误的数据得到错误的模型”的根本问题.为此,提出用数据包络分析(DEA)优化偏最小二乘同归的建模方法,用DEA方法对数据进行评价,剔除无效数据,将有效的数据用来偏最小二乘回归建模.该方法能有效克服干扰数据对提取成分的影响,弥补偏最小二乘方法的不足.通过实例计算并与PLSR、主成分回归(PCR)比较分析表明:DEA优化偏最小二乘回归建模平均绝对误差为2.66％,低于PLSR的4.07％和PCR的4.45％.%The partial least squares regression (PLSR) statistical modeling approach estimates the average trend of the data essentially, which cannot avoid the problem that obtain the wrong model according to the error data. Aim at this problem, the optimized PLSR with data envelopment analysis (DEA) was proposed to overcome this problem, which could evaluate the efficiency of the data and remove the inefficiency data for the PLSR modeling. The new approach can overcome the effect of the disturbed data when filtering principal components in the independent variables. Comparing with the principal component regression (PCR) and the PLSR with computing example, the average absolute error of the optimized the PLSR with DEA was 2. 66% .which was much lower than PLSR with 4. 07% and the PCR with 4. 45%.