中文说明:应用背景长期以来,模型式的方法和认识性的方法之间的界限分得十分清楚。而偏最小二乘法则把它们有机的结合起来了,在一个算法下,可以同时实现回归建模(多元线性回归)、数据结构简化(主成分分析)以及两组变量之间的相关性分析(典型相关分析)。这是多元统计数据分析中的一个飞跃。关键技术作为一个多元线性回归方法,偏最小二乘回归的主要目的是要建立一个线性模型:Y=XB+E,其中Y是具有m个变量、n个样本点的响应矩阵,X是具有p个变量、n个样本点的预测矩阵,B是回归系数矩阵,E为噪音校正模型,与Y具有相同的维数。在通常情况下,变量X和Y被标准化后再用于计算,即减去它们的平均值并除以标准偏差。
English Description:
Application backgroundFor a long time, the boundary between the method and the method of the model is very clear. And the partial least squares algorithm to combine them organically, in an algorithm, can simultaneously realize the regression model (multiple linear regression), data structure simplification (principal component analysis) and the correlation analysis between the two groups of variables (canonical correlation analysis). This is a leap in multivariate statistical data analysis.Key TechnologyAs a multiple linear regression method, the main purpose of partial least squares regression is to establish a linear model: Y=XB+E, where Y is a response matrix with m variables, n sample points, X is a p variable, n is the prediction matrix, B is the regression coefficient matrix, E is the noise correction model, and Y has the same dimension. In normal circumstances, the variables X and Y are used to calculate, that is, the average value of t