正交偏最小二乘我要分享

Orthogonal partial least squares

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中文说明: PLS是用线性回归模型和最小二乘法把X(描述性变量)和Y(观察变量)投射到一个新的空间,从而能在X空间中的找到一个多维向量最大化表示出Y空间上的变化,找到X和Y最根本的联系。 正交偏最小二乘法(OPLS)是基于PLS的,把连续的变量正交(orthogonal) 投射到 latent structure,从而把变量分成了可以预测的和无关的两种,第一个latent variable可以解释X和Y之间的共同变化,也就是X中变化跟Y变化有关的,第二之后的latent variable是在X变化中对Y无关的(正交的)。如果是不连续的变量,就可以对不同的class进行分类,就是OPLS-DA。X是描述性变量的矩阵,Y是不同的class种类,同样的,第一个latent variable描述的是X中对between class有关联的变化,也就是X对Y分类有关的信息,后面与之正交的latent varible 描述的都是X中within class之间的变化,也就是对Y的分类无关。OPLS相比PLS,分类的准确率并没有改进,只是让结果能更好的被诠释和理解而已


English Description:

PLS is to project x (descriptive variable) and Y (observation variable) into a new space by using linear regression model and least square method, so as to find a multidimensional vector in X space, maximize the change in Y space, and find the most fundamental relationship between X and y. Orthogonal partial least squares (OPLS) is based on PLS, which projects continuous orthogonal variables to the late structure, thus dividing the variables into predictable and irrelevant ones. The first late variable can explain the common change between X and y, that is, the change in X is related to the change in Y, and the second late variable can explain the common change between X and y Variable is independent of Y (orthogonal) in X variation. If it is a discontinuous variable, you can classify different classes, which is opls-da. X is a matrix of descriptive variables, and Y is a different class type. Similarly, the first late variable describes the changes related to the between class in X, that is, the information related to the classification of X to y. the later orthogonal late variable describes the changes between classes in X, that is, the classification of Y is irrelevant. Compared with PLS, OPLS does not improve the accuracy of classification, but makes the results better interpreted and understood


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