回归建模 Resources

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Partial Least Squares Regression (PLSR) represents a novel multivariate statistical analysis method focused on regression modeling between multiple dependent and independent variables. This approach proves particularly effective when dealing with highly linearly correlated variables and efficiently handles scenarios where the number of samples is smaller than the number of variables. MATLAB implementation typically involves dimensionality reduction through iterative projection algorithms.

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Application Background For a long time, there has been a clear distinction between model-based methods and epistemological approaches. Partial Least Squares (PLS) organically integrates these two methodologies, enabling simultaneous implementation of regression modeling (multivariate linear regression), data structure simplification (principal component analysis), and correlation analysis between two variable sets (canonical correlation analysis) within a single algorithm. This represents a significant breakthrough in multivariate statistical data analysis. Key Technology As a multivariate linear regression method, the primary objective of PLS regression is to establish a linear model: Y=XB+E, where Y is the response matrix with m variables and n sample points, X is the predictor matrix with p variables and n sample points, B is the regression coefficient matrix, and E represents the noise correction model with the same dimensions as Y. Typically, variables X and Y are standardized before computation by subtracting their means and dividing by standard deviations.

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