Orthogonal projections to latent structures (OPLS) is a new multivariate statistical method, which was first proposed by Johan Tryggde et al. in 2002. In the past ten years, this method has been rapidly developed in theory and application, and has a large number of applications in metrology chemistry. OPLS is a regression modeling method of multiple dependent variables to multiple independent variables. Its biggest feature is that it can remove the data variation that has nothing to do with the categorical variables, so that the categorical information is mainly concentrated in one principal component, so that the model changes It must be simple and easy to explain, and the discriminant effect and the visualization effect of the principal component score map are more obvious.
OPLS removes the orthogonal variables of the system from the given data set X and distinguishes these orthogonal variables from non-orthogonal variables. These orthogonal variables can be analyzed separately. The OPLS method uses the information of the response variable to divide it into three parts.
x= TpP1p+ ToPo+ E
That is, Tp represents the predicted score matrix, PT represents the predicted load matrix of X, TpPT represents the predicted part, To represents the score matrix of the orthogonal component of the row (called OPLS component), PT represents the corresponding load matrix, ToPT o Represents the part orthogonal to Y, and E is the residual matrix.
The abscissa of the OPLS-DA score chart represents the score value (Tp) of the main component in the OSC process, so the difference between the groups can be seen from the direction of the abscissa; the ordinate represents the score of the orthogonal component in the OSC process Value (TO); Therefore, the difference within the group (the difference between samples within the group) can be seen from the ordinate.
Figure 1. OPLS-DA score chart.
The abscissa of the S-plot graph represents the co-correlation coefficient of the main component and metabolites, and the ordinate represents the correlation coefficient of the main component and metabolites. S-plot is generally used to select metabolites that have a strong correlation with the main components in the OSC process. On the other hand, it is also possible to select metabolites that have a strong correlation with Y. The metabolites closer to the two corners are more important. The red points indicate that the VIP values of these metabolites are greater than or equal to 1, and the green points indicate that the VIP values of these metabolites are less than or equal to 1.
Figure 2. OPLS-DA s-plot.
The abscissa of the model verification permutation Test graph represents the accuracy of the model, the ordinate represents the frequency of the accuracy of 200 models in 200 permutation Tests, and the arrow represents the location of the accuracy of the OPLS-DA model. R2X and R2Y represent the accuracy of the model. The interpretation rate of the X and Y matrices of the built model, Q2 represents the predictive ability of the model. In theory, the closer the R2 and Q values are to 1, the better the model.
Figure 3. OPLS-DA verification diagram.
Many variables of partial least squares are used to estimate the factors and loading matrices T, U, P, and Q. Most of them construct a linear regression estimate Y=XB+Bo between X and Y. Some partial least squares algorithms are only suitable for the case where Y is a column vector, while other algorithms deal with the general case where Y is a matrix. The algorithm also differs according to whether they estimate the factor matrix T as an orthogonal matrix. The final prediction is the same in all different least square algorithms, but the components are different.
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