OnPLS-a novel multiblock method for the modelling of predictive and orthogonal variation

Journal of Chemometrics

Volumn 25, Issue 8, 2011, Pages 441-455

  Löfstedt, Tommy ^a   Trygg, Johan ^a  

^a UMEÅ UNIVERSITY   (Sweden)

Author keywords

Multiblock analysis; O2PLS; OnPLS; Orthogonal projections to latent structures; PLS

Indexed keywords

ANALYSIS METHOD; MATRIX; MULTIBLOCK ANALYSIS; MULTIBLOCKS; O2PLS; ONPLS; ORTHOGONAL PROJECTION; ORTHOGONAL PROJECTION TO LATENT STRUCTURE; PLS; PROJECTION TO LATENT STRUCTURES;

MATRIX ALGEBRA;

EID: 80051934386     PISSN: 08869383     EISSN: 1099128X     Source Type: Journal    
DOI: 10.1002/cem.1388     Document Type: Article

References (51)

1. Hotelling H. The most predictable criterion. J. Educ. Psychol. 1935; 26: 139-142.
2. Hotelling H. Relations between two sets of variates. Biometrika 1936; 28: 321-377.
3. Horst P. Relations among m sets of measures. Psychometrika 1961; 26(2): 129-149.
4. Horst P. Generalized canonical correlations and their applications to experimental data. J. Clin. Psychol. 1961; 17(4): 331-347.
5. Horst P. Factor Analysis of Data Matrices. Holt, Rinehart and Winston: New York, 1965.
6. Steel RGD. Minimum generalized variance for a set of linear functions. Ann. Math. Stat. 1951; 22(3): 456-460.
7. Carroll JD. Generalization of canonical correlation analysis to three or more sets of variables. Proceeding of the 76th Convention of the American Psychological Association, 1968; 227-228.
8. Kettenring JR. Canonical analysis of several sets of variables. Biometrika 1971; 58(3): 433-451.
9. Van de Geer JP. Linear relations among k sets of variables. Psychometrika 1984; 49(1): 79-94.
10. ten Berge JMF. A general solution for the MAXBET problem. In Multidimensional Data Analysis, De Leeuw WJ, Heiser J, Meulman J, Critchley F (eds). DSWO Press: Leiden, 1986; 81-87.
11. ten Berge JMF. Generalized approaches to the MAXBET problem and the MAXDIFF problem, with applications to canonical correlations. Psychometrika 1988; 53(4): 487-494.
12. Tucker LR. An inter-battery method of factor analysis. Psychometrika 1958; 23(2): 111-136.
13. Michel T, EspositoVinzi V, Chatelin Y-M, Lauro C. PLS path modeling. Comput. Stat. Data Anal. 2005; 48(1): 159-205.
14. Wold H. Partial least squares. In Encyclopedia of Statistical Sciences, vol. 6, Kotz S, Johnson NL (eds). Wiley: New York, 1985; 581-591.
15. Wold H. Nonlinear estimation by iterative least square procedures. In Research Papers in Statistics: Festschrift for J. Neyman, David FN (ed.). Wiley: London, 1966; 411-444.
16. Wold H. Estimation of principal components and related models by iterative least squares. In Multivariate Analysis, Krishnaiah PR (ed.). Academic Press: New York, 1966; 391-420.
17. Wold S, Martens H, Wold H. The multivariate calibration problem in chemistry solved by the PLS method. Lect. Notes Math. 1983; 973: 286-293.
18. Tenenhaus M, Hanafi M. A bridge between PLS path modeling and multi-block data analysis. In Handbook of Partial Least Squares: Concepts, Methods and Applications, Esposito Vinzi V, Chin WW, Henseler J, Wang H (eds). Springer: Berlin, 2010.
19. Tenenhaus M, EspositoVinzi V. PLS regression, PLS path modeling and generalized procrustean analysis: a combined approach for multiblock analysis. J. Chemom. 2005; 19(3): 145-153.
20. Wold H. Nonlinear iterative partial least squares (NIPALS) modelling: some current developments. In Multivariate Analysis, Krishnaiah PR (ed.). Academic Press: New York, 1973; 383-407.
21. Wold H. Soft modelling by latent variables: the non-linear iterative partial least squares (NIPALS) approach. In Perspectives in Probability and Statistics, Gani J (ed.). Academic, Applied Probability Trust: London, 1975, 117-142.
22. Hanafi M, Kiers HAL. Analysis of k sets of data, with differential emphasis on agreement between and within sets. Comput. Stat. Data Anal. 2006; 51(3): 1491-1508.
23. Van Deun K, Smilde A, vander Werf M, Kiers H, Van Mechelen I. A structured overview of simultaneous component based data integration. BMC Bioinformatics 2009; 10(1): 246-261.
24. Ten Berge JMF, Kiers HAL, Van der Stel V. Simultaneous component analysis. Statistica Applicata 1992; 4: 277-392.
25. Smilde AK, Westerhuis JA, de Jong. S. A framework for sequential multiblock component methods. J. Chemom. 2003; 17(6): 323-337.
26. Casin P. A generalization of principal component analysis to K sets of variables. Comput. Stat. Data Anal. 2001; 35(4): 417-428.
27. Wold S, Kettaneh N, Tjessem K. Hierarchical multiblock PLS and PC models for easier model interpretation and as an alternative to variable selection. J. Chemom. 1996; 10: 463-482.
28. Wold S, Antti H, Lindgren F, Ohman J. Orthogonal signal correction of near-infrared spectra. Chemom. Intel. Lab. Syst. 1998; 44: 175-185.
29. Trygg J, Wold S. Orthogonal projections to latent structures (O-PLS). J. Chemom. 2002; 15: 1-18.
30. Trygg J. O2-PLS for qualitative and quantitative analysis in multivariate calibration. J. Chemom. 2002; 16: 283-293.
31. Trygg J, Wold S. O2-PLS, a two-block (X-Y) latent variable regression (LVR) method with an integral OSC filter. J. Chemom. 2003; 17: 53-64.
32. Bylesjo M, Nilsson R, Srivastava V, Gronlund A, Johansson AI, Jansson S, Karlsson J, Moritz T, Wingsle G, Trygg J. Integrated analysis of transcript, protein and metabolite data to study lignin biosynthesis in hybrid aspen. J. Proteome Res. 2009; 8(1): 199-210.
33. Hoskuldsson A. PLS regression methods. J. Chemom. 1988; 2(3): 211-228.
34. Hoskuldsson A. Prediction Methods in Science and Technology. (1st edn). Thor Publishing: Copenhagen, 1996.
35. Wold S, Sjostrom M, Eriksson L. PLS-regression: a basic tool of chemometrics. Chemom. Intel. Lab. Syst. 2001; 58(2): 109-130.
36. Hanafi M, ten Berge J. Global optimality of the successive MAXBET algorithm. Psychometrika 2003; 68: 97-103.
37. Martens H, Naes T. Multivariate Calibration. Wiley: Chichester, 1989.
38. Fearn T. On orthogonal signal correction. Chemom. Intel. Lab. Syst. 2000; 50: 47-52.
39. Hoskuldsson A. Variable and subset selection in PLS regression. Chemom. Intel. Lab. Syst. 2001; 55: 23-38.
40. Sjoblom J, Svensson O, Josefsson M, Kullberg H, Wold S. An evaluation of orthogonal signal correction applied to calibration transfer of near infrared spectra. Chemom. Intel. Lab. Syst. 1998; 44: 229-244.
41. Andersson CA. Direct orthogonalization. Chemom. Intel. Lab. Syst. 1999; 47: 51-63.
42. Westerhuis JA, deJong S, Smilde AK. Direct orthogonalization signal correction. Chemom. Intel. Lab. Syst. 2001; 56: 13-25.
43. Kvalheim OM, Rajalahti T, Arneberg R. X-tended target projection (XTP)-comparison with orthogonal partial least squares (OPLS) and PLS post-processing by similarity transformation (PLS+ST). J. Chemom. 2009; 23(1): 49-55.
44. Yu H, MacGregor JF. Post processing methods (PLS-CCA): Simple alternatives to preprocessing methods (OSC-PLS). Chemom. Intel. Lab. Syst. 2004; 73(2): 199-205.
45. Ergon R. PLS post-processing by similarity transformation (PLS+ST): a simple alternative to OPLS. J. Chemom. 2005; 19(1): 1-4.
46. Kemsley EK, Tapp. HS. OPLS filtered data can be obtained directly from non-orthogonalized PLS1. J. Chemom. 2009; 23(5): 263-264.
47. Golub Gene H, Van Loan CF. Matrix Computations, (3rd edn). Johns Hopkins University Press: Baltimore, MD, USA, 1996.
48. Alter O, Brown PO, Botstein D. Generalized singular value decomposition for comparative analysis of genome-scale expression data sets of two different organisms. Proc. Natl. Acad. Sci. USA 2003; 100(6): 3351-3356.
49. Flury B. Two generalizations of the common principal component model. J. Am. Stat. Assoc. 1987; 74(1): 59-69.
50. Flury B. Common principal components in k groups. J. Am. Stat. Assoc. 1984; 79(388): 892-898.
51. Smilde AK, Kiers HAL, Bijlsma S, Rubingh CM, van Erk. MJ. Matrix correlations for high-dimensional data: the modified RV-coefficient. Bioinformatics 2009; 25(3): 401-405.