Discriminant partial least squares analysis on compositional data

Statistical Modelling

Volumn 10, Issue 1, 2010, Pages 41-56

  Gallo, Michele ^a  

^a University of Naples L'Orientale   (Italy)

Author keywords

Aitchison distance; Compositional observation; Discriminant analysis; Log contrast; Partial least squares

Indexed keywords

EID: 77950523040     PISSN: 1471082X     EISSN: 14770342     Source Type: Journal    
DOI: 10.1177/1471082X0801000103     Document Type: Article

References (19)

1. Aitchison J (1982) The statistical analysis of compositional data (with discussion). Statistical Methodology, 44, 139-77.
2. Aitchison J (1986) The statistical analysis of compositional data. London: Chapman & Hall.
3. Aitchison J (1992) On criteria for measures of compositional difference. Mathematical Geology, 22, 223-26.
4. Aitchison J and Greenacre M (2002) Biplots for compositional data. Applied Statistics, 51, 375-92.
5. Barceló-Vidal C, Martín-Fernández JA and Pawlowsky-Glahn V (2001) Mathematical foundations of compositional data analysis. In Ross G ed. Proceedings of IAMG'01- the sixth annual conference of the International Association for Mathematical Geology. Electronic publication.
6. Barker M and Rayens W (2003) Partial least squares for discrimination. Journal of Chemometrics, 17, 166-73.
7. Baxter MJ (1995) Standardization and transformation in principal component analysis, with applications to archaeometry. Applied Statistics, 44, 513-27.
8. de Jong S (1993) SIMPLS: an alternative approach to partial least squares regression. Chemometrics and Intelligent Laboratory Systems, 33, 251-63.
9. de Jong S and ter Braak CJF (1994) Comments on the PLS kernel algorithm. Journal of Chemometrics, 22, 169-74.
10. Frank I and Friedman J (1993) A statistical views of some chemometrics regression tools. Technometrics, 35, 109-48.
11. Gallo M (2003) Partial least squares for compositional data: an approach based on the splines. Italian Journal of Applied Statistics, 15, 349-58.
12. Gallo M and Mahdi S (2008). Discriminant partial least square on compositional data: a comparison with the log-contrast principal component analysis. Proceedings of MTISD 2008. Methods, Models and Information Technologies for Decision Support Systems (Ciavolini, et al.eds) LECCE, SIBA, pp. 45-48.
13. Hinkle J and Rayens W (1995) Partial least squares and compositional data: problems and alternatives. Chemometrics and Intelligent Laboratory Systems, 30,159-72.
14. Martin-Fernandez JA, Barcelo-Vidal C and Pawlowsky-Glahn V (1998) Measures of difference for compositional data and hierarchical clustering. Proceedings of IAMG'98 (Bucånti,G.Nardi, and R. Potenza eds). Napoli Italy: De Frede Editore, 526-31.
15. Mooijaart A, Van Der Heijden PGM and Van Der Ark LA (1999) A least squares algorithm for a mixture model for compositional data. Computational Statistics and Data Analysis, 30, 359-79.
16. Rayens W (2000) The art of maximizing covariance. University of Kentucky Technical Report 383.
17. Tenenhaus M (1998) La régression PLS. Théorie et pratique. Paris: Editions Technip.
18. Wold H (1966) Estimation of principal components and related models by iterative least squares. In PR Krishnaiaah ed. Multivariate analysis. New York: Academic Press, 391-420.
19. Wold H (1975) Soft modelling by latent variables: the nonlinear iterative partial least squares (NIPALS) approach. In Honor of M. S. Bartlett-(Gani ed.) Perspectives in Probability and Statistics. London: Academic Press, 117-44.