Elements of Simplicial Linear Algebra and Geometry

Compositional Data Analysis: Theory and Applications

Volumn , Issue , 2011, Pages 139-157

  Egozcue, Juan José ^a   Barceló Vidal, Carles ^b   Martín Ferńandez, Josep Antoni ^b   Jarauta Bragulat, Eusebi ^a   Díaz Barrero, José Luis ^a   Mateu Figueras, Glòria ^b  

^a UNIVERSITY OF GIRONA   (Spain)

^b UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

Aitchison geometry, and development of new tools representation of compositions; Centred log ratio representation different ways of representing a composition; Concepts of Euclidean spaces adapted to simplex, perturbation and powering operations and Aitchison metric use; Elementary concepts Euclidean character of the Aitchison geometry of the simplex; Elements of simplicial geometry n part simplex; Linear functions, between Euclidean spaces part of general theory, using coordinate expressions; Linear functions simplex with perturbation, the Aitchison metrics, Euclidean space; Theory, algebra and calculus elements of simplicial linear algebra and geometry; Use of simplex as a sample space of compositional data; Vector space Aitchison (1986), introducing perturbation between elements of n part simplex

Indexed keywords

EID: 84872412884     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1002/9781119976462.ch11     Document Type: Chapter

References (15)

1. Aitchison J 1982 The statistical analysis of compositional data (with discussion). Journal of the Royal Statistical Society, Series B (Statistical Methodology) 44(2), 139-177.
2. Aitchison J 1983 Principal component analysis of compositional data. Biometrika 70(1), 57-65.
3. Aitchison J 1986 The Statistical Analysis of Compositional Data.Monographs on Statistics and Applied Probability. Chapman and Hall Ltd (reprinted 2003 with additional material by The Blackburn Press), London (UK). 416 p.
4. Aitchison J 1992 On criteria for measures of compositional difference. Mathematical Geology, 24(4), 365-379.
5. Aitchison J and Egozcue JJ 2005 Compositional data analysis: where are we and where should we be heading?. Mathematical Geology 37(7), 829-850.
6. Aitchison J, Barceló-Vidal C, Martín-Fernández JA and Pawlowsky-Glahn V 2001 Reply to Letter to the Editor by S. Rehder and U. Zier. Mathematical Geology 33(7), 849-860.
7. Barceló-Vidal C, Martín-Fernández JA and Pawlowsky-Glahn V 2001 Mathematical foundations of compositional data analysis. In Proceedings of IAMG'01-The VII Annual Conference of the International Association for Mathematical Geology (ed. Ross G). Kansas Geological Survey, Cancun (Mexico). p. 20.
8. Billheimer D, Guttorp P and FaganW2001 Statistical interpretation of species composition. Journal of the American Statistical Association 96(456), 1205-1214.
9. Egozcue JJ and Pawlowsky-Glahn V 2005 Groups of parts and their balances in compositional data analysis. Mathematical Geology 37(7), 795-828.
10. Egozcue JJ and Pawlowsky-GlahnV2006 Simplicial geometry for compositional data. In Compositional Data Analysis in the Geosciences: From Theory to Practice. Geological Society, London (UK). pp. 145-159.
11. Egozcue JJ, Pawlowsky-Glahn V, Mateu-Figueras G and Barceló-Vidal C 2003 Isometric logratio transformations for compositional data analysis. Mathematical Geology 35(3), 279-300.
12. Gantmacher FR 1959 The Theory of Matrices, vol. 2. Chelsea Publishing Co., New York, NY (USA). 276 p.
13. Pawlowsky-Glahn V and Egozcue JJ 2001, Geometric approach to statistical analysis on the simplex. Stochastic Environmental Research and Risk Assessment (SERRA) 15(5), 384-398.
14. Thió-Henestrosa S, Egozcue JJ, Pawlowsky-Glahn V, Kovács LO and Kovács G 2008 Balancedendrogram. a new routine of codapack. Computer and Geosciences 34(12), 1682-1696.
15. Tolosana-Delgado R, Pawlowsky-Glahn V and Egozcue JJ 2008 Indicator kriging without order relation violations. Mathematical Geosciences 40, 327-347.