Re-interpretation of NIPALS results solves PLSR inconsistency problem

Journal of Chemometrics

Volumn 23, Issue 2, 2009, Pages 72-75

  Ergon, Rolf ^a  

^a UNIVERSITY OF SOUTH EASTERN NORWAY   (Norway)

Author keywords

Model inconsistency; NIPALS; Orthogonalization; PLSR

Indexed keywords

INVERSE PROBLEMS; LEAST SQUARES APPROXIMATIONS;

GENERALIZED INVERSE; MODEL INCONSISTENCY; MODEL SPACES; NONLINEAR ITERATIVE PARTIAL LEAST SQUARE; ORTHOGONALIZATION; OUTLIER DETECTION; PARTIAL LEAST SQUARE ALGORITHMS; PARTIAL LEAST SQUARE REGRESSION; PARTIAL LEAST-SQUARES; SIMPLE++;

ITERATIVE METHODS;

EID: 60149091010     PISSN: 08869383     EISSN: 1099128X     Source Type: Journal    
DOI: 10.1002/cem.1180     Document Type: Article

References (14)

1. Pell RJ, Ramos LS, Manne R. The model space in partial least squares regression. J. Chemom. 2007; 21: 165-172.
2. Martens H. Reliable and relevant modelling of real world data: a personal account of the development of PLS Regression. Chemom. Intell. Lab. Syst. 2001; 58: 85-95.
3. Wold S, Martens H, Wold H. The multivariate calibration problem in chemistry solved by the PLS method. In: Matrix Pencils. Springer Verlag: Heidelberg, 1982; 286-293.
4. Martens H, Næs T. Multivariate calibration by data compression. Near-infrared Technology in Agricultural and Food Industries. The American Association of Cereal Chemists: St. Paul, Minnesota, 1987; 57-87.
5. Ergon R. PLS score-loading correspondence and a bi-orthogonal factorization. J. Chemom. 2002; 16: 368-373.
6. Helland IS. On the structure of partial least squares regression. Commun. Stat. 1988; 17: 581-607.
7. Golub GH, Kahan W. Calculating the singular values and pseudoinverse of a matrix. SIAM J. Scientific. Comput. 1984; 2: 205-224.
8. Ergon R. Dynamic system multivariate calibration. Chemom. Intell. Lab. Syst. 1998; 44: 135-146.
9. Ergon R. Noise handling capabilities of multivariate calibration methods. Model. Identif. Contol 2002; 23: 259-273.
10. Ergon R. Finding Y-relevant parts of X by use of PCR and PLSR model reduction methods. J. Chemom. 2007; 21: 537-546.
11. Martens H, Næs T. Multivariate Calibration. Wiley: New York, 1989.
12. Golub GH, Van Loan CF. Matrix Computations. The Johns Hopkins University Press: Baltimore, 1996.
13. Manne R. Analysis of two partial-least-squares algorithms for multivariate calibration. Chemom. Intell. Lab. Syst. 1987; 2: 187-197.
14. Ergon R, Esbensen KH. A didactically motivated PLS algorithm. Model. Identif. Control 2001; 22: 131-13.