改进的偏最小二乘回归模型及应用

Nonlinear Partial Least Squares Regression Model Based on Stacking Integration and its Application

对样本量小于特征数量的高维数据进行拟合时,偏最小二乘回归模型(PLS)因自身优点对线性关系的拟合效果较好。为解决PLS模型对非线性关系拟合效果较差并控制模型计算量两方面问题,提出基于stacking集成非线性偏最小二乘模型(stacking-plsr)。从模型鲁棒性、敏感性和拟合精度三个方面对stacking-plsr模型进行实证检验。结果表明,stacking-plsr模型的拟合效果对训练集样本数量和超参数degree的取值并不敏感,在测试集上预测值的MSE和ARE两项指标相较于传统PLS模型分别降低68.26%和34.44%。

When fitting the high-dimensional data whose sample size is less than the number of features,the partial least squares regression model(PLS)has better fitting effect on the linear relationship due to its own advantages.In order to solve the two problems of PLS model's poor fitting effect on the nonlinear relationship and control the calculation amount of the model,a nonlinear partial least squares model based on the stacking(stacking-plsr)is proposed.The stacking-plsr model is empirically tested from three aspects of model robustness,sensitivity and fitting accuracy.The results show that the fitting effect of the stacking-plsr model is not sensitive to the number of training samples and the value of the super parameter degree.The MSE and ARE of the prediction results of the test set are 68.26%and 34.44%lower than those of the PLS model respectively.