NIPALS Algorithm with Leave-One-Out Cross-Validation Plotting

The current text provides a brief mention of the NIPALS (Nonlinear Iterative Partial Least Squares) algorithm, which is an efficient method for estimating multivariate models particularly useful in chemometrics and multivariate data analysis. The algorithm operates through an iterative process that identifies principal components by successively approximating the input matrix using orthogonal projections. In code implementation, this typically involves initializing with random vectors, then iteratively calculating scores and loadings until convergence criteria are met. The reference to "留1法" corresponds to the leave-one-out cross-validation technique, a robust method for assessing model performance. This validation approach systematically excludes one observation from the dataset, trains the model on the remaining n-1 samples, and evaluates predictive accuracy on the omitted observation. This process repeats for all data points, providing comprehensive performance metrics. The mention of "交叉检验绘图" refers to cross-validation plotting visualization, which typically displays metrics like RMSE (Root Mean Square Error) or Q² values against the number of components. These plots help determine the optimal number of principal components by showing where adding more components stops improving prediction accuracy. In practice, such visualizations are created using plotting libraries that graph cross-validation results against component count, often incorporating confidence intervals or error bars to indicate stability of the estimates. For implementation, key functions would include iterative matrix decomposition for NIPALS, systematic data partitioning for cross-validation, and visualization routines for result interpretation. The algorithm's efficiency makes it particularly suitable for high-dimensional datasets where traditional PCA methods might be computationally intensive.