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

Chemometrics and Intelligent Laboratory Systems 51 2000 145–161 locatechemometrics Fast regression methods in a Lanczos or PLS-1 basis. Theory and applications Wen Wu a,1, Rolf Manne b, a ChemoAC, Pharmaceutical Institute, Vrije Uniersiteit Brussel, Laarbeeklaan 103, B-1090 Brussel, Belgium b Department of Chemistry, Uniersity of Bergen, Allegt 41, NO-5007 Bergen, Norway Received 4 October 1999; received in revised form 3 February 2000; accepted 15 February 2000 Abstract In order to improve the calibration speed for very large data sets, novel algorithms for principal component regression PCR and partial-least-squares PLS regression are presented. They use the Lanczos or PLS-1 transformation to reduce the data matrix X to a small bidiagonal matrix R , after which the small tridiagonal matrix R R is diagonalized and inverted. The complexity of the PCR model may be optimized by cross-validation PCRL but also using simpler and faster recipes based upon round-off monitoring and model fit PCRF . A similar fast PLS procedure PLSF is also presented. Calculations are made for five near infrared spectroscopy NIR data sets and compared with PCR with feature selection PCRS based on correlation and with de Jong’s simple partial least squares SIMPLS . The Lanczos-based met