Kernel-PCA algorithms for wide data Part II: Fast cross-validation and application in classification of NIR data

Four PCA algorithms, namely NIPALS, the power method (POWER), singular value decomposition (SVD) and eigenvalue decomposition (EVD), and their kernel versions are systematically applied to three NIR data sets from the pharmaceutical industry. Cross-validation is used to determine the number of PC factors needed as the input for linear discriminant analysis (LDA). LDA with PCA as the dimension reduction method successfully classifies all three data sets. The kernel algorithms are faster than their corresponding classic algorithms. Of the four classic algorithms, SVD is the fastest. When only the first few PCs are desired, the kernel-POWER method is the fastest of all the algorithms. When all PCs are required, EVD is the most efficient of the four kernel algorithms. When cross-validation is applied, kernel-EVD greatly reduces the elapsed time compared to the classic algorithms. To further speed up cross-validation, two matrix updating methods are proposed. Compared to the normal cross-validation procedure, the first method slightly improves the speed of cross-validation by using the normal kernel-EVD. The second method greatly speeds up cross-validation, but needs a modified kernel-EVD algorithm.