Fast regression methods in a Lanczos (or PLS-1) basis. Theory and applications

In order to improve the calibration speed for very large data sets, novel a lgorithms for principal component regression (PCR) and partial-least-square s (PLS) regression are presented. They use the Lanczos or PLS-1 transformat ion to reduce the data matrix X to a small bidiagonal matrix (R), after whi ch the small tridiagonal matrix (R'R) is diagonalized and inverted. The com plexity of the PCR model may be optimized by cross-validation (PCRL) but al so using simpler and faster recipes based upon sound-off monitoring and mod el fit (PCRF). A similar fast PLS procedure (PLSF) is also presented. Calcu lations are made for five near infrared spectroscopy (NIR) data sets and co mpared with PCR with feature selection (PCRS) based on correlation and with de Jong's simple partial least squares (SIMPLS). The Lanczos-based methods have comparable prediction performance and similar model complexity to PCR S and SIMPLS but are considerably faster. From a detailed comparison of the methods, some insight is gained into the performance of the PLS method. (C ) 2000 Elsevier Science B.V. All rights reserved.