메뉴 건너뛰기




Volumn 37, Issue 7, 2005, Pages 829-850

Compositional data analysis: Where are we and where should we be heading?

Author keywords

Hilbert and euclidean space; Regression; Sample space; Simplex geometry; Stay in the simplex; Subcomposition

Indexed keywords

DATA REDUCTION; GEOMETRY; PROBLEM SOLVING; REGRESSION ANALYSIS;

EID: 33646261413     PISSN: 08828121     EISSN: 15738868     Source Type: Journal    
DOI: 10.1007/s11004-005-7383-7     Document Type: Article
Times cited : (292)

References (75)
  • 1
    • 0343861965 scopus 로고
    • A new approach to null correlations of proportions
    • Aitchison, J., 1981, A new approach to null correlations of proportions: Math. Geol., v. 13, no. 2, p. 175-189.
    • (1981) Math. Geol. , vol.13 , Issue.2 , pp. 175-189
    • Aitchison, J.1
  • 2
    • 0001218562 scopus 로고
    • The statistical analysis of compositional data (with discussion)
    • Aitchison, J., 1982, The statistical analysis of compositional data (with discussion): J. R. Stat. Soc., Ser. B (Stat. Methodol.), v. 44, no. 2, p. 139-177.
    • (1982) J. R. Stat. Soc. Ser. B (Stat. Methodol.) , vol.44 , Issue.2 , pp. 139-177
    • Aitchison, J.1
  • 3
    • 0002769176 scopus 로고
    • Principal component analysis of compositional data
    • Aitchison, J., 1983, Principal component analysis of compositional data: Biometrika, v. 70, no. 1, p. 57-65.
    • (1983) Biometrika , vol.70 , Issue.1 , pp. 57-65
    • Aitchison, J.1
  • 4
    • 15844366330 scopus 로고
    • The statistical analysis of geochemical compositions
    • Aitchison, J., 1984, The statistical analysis of geochemical compositions: Math. Geol., v. 16, no. 6, p. 531-564.
    • (1984) Math. Geol. , vol.16 , Issue.6 , pp. 531-564
    • Aitchison, J.1
  • 5
    • 0001420825 scopus 로고
    • A general class of distributions on the simplex
    • Aitchison, J., 1985, A g]eneral class of distributions on the simplex: J. R. Stat. Soc., Ser. B (Stat. Methodol.), v. 47, no. 1, p. 136-146.
    • (1985) J. R. Stat. Soc. Ser. B (Stat. Methodol.) , vol.47 , Issue.1 , pp. 136-146
    • Aitchison, J.1
  • 6
    • 0003671433 scopus 로고
    • The statistical analysis of compositional data
    • Monographs on Statistics and Applied Probability: Chapman & Hall, London (Reprinted in 2003 with additional material by Blackburn Press)
    • Aitchison, J., 1986, The statistical analysis of compositional data. Monographs on statistics and applied Probability: Chapman & Hall, London (Reprinted in 2003 with additional material by Blackburn Press), 416 p.
    • (1986) , pp. 416
    • Aitchison, J.1
  • 7
    • 0025638328 scopus 로고
    • Relative variation diagrams for describing patterns of compositional variability
    • Aitchison, J., 1990, Relative variation diagrams for describing patterns of compositional variability: Math. Geol., v. 22, no. 4, p. 487-511.
    • (1990) Math. Geol. , vol.22 , Issue.4 , pp. 487-511
    • Aitchison, J.1
  • 8
    • 0026459054 scopus 로고
    • On criteria for measures of compositional difference
    • Aitchison, J., 1992a, On criteria for measures of compositional difference: Math. Geol., v. 24, no. 4, p. 365-379.
    • (1992) Math. Geol. , vol.24 , Issue.4 , pp. 365-379
    • Aitchison, J.1
  • 9
    • 33646228580 scopus 로고
    • The triangle in statistics
    • Mardia, K., ed. A tribute to G. S. Watson: Wiley, New York
    • Aitchison, J., 1992b, The triangle in statistics, in Mardia, K., ed., The art of statistical science. A tribute to G. S. Watson: Wiley, New York, p. 89-104.
    • (1992) The Art of Statistical Science , pp. 89-104
    • Aitchison, J.1
  • 11
    • 0002198040 scopus 로고    scopus 로고
    • The one-hour course in compositional data analysis or compositional data analysis is simple
    • Pawlowsky-Glahn, V., ed. Vol. I, II and addendum: International Center for Numerical Methods in Engineering (CIMNE), Barcelona, Spain
    • Aitchison, J., 1997, The one-hour course in compositional data analysis or compositional data analysis is simple, in Pawlowsky-Glahn, V., ed., Proceedings of IAMG'97 - The third annual conference of the International Association for Mathematical Geology, Vol. I, II and addendum: International Center for Numerical Methods in Engineering (CIMNE), Barcelona, Spain, p. 3-35.
    • (1997) Proceedings of IAMG'97 - The Third Annual Conference of the International Association for Mathematical Geology , pp. 3-35
    • Aitchison, J.1
  • 12
    • 0032768141 scopus 로고    scopus 로고
    • Logratios and natural laws in compositional data analysis
    • Aitchison, J., 1999, Logratios and natural laws in compositional data analysis: Math. Geol., v. 131, no. 5, p. 563-580.
    • (1999) Math. Geol. , vol.131 , Issue.5 , pp. 563-580
    • Aitchison, J.1
  • 13
    • 0742297285 scopus 로고    scopus 로고
    • Simplicial inference
    • Viana, M.A.G., and Richards, D.S.P., eds. Contemporary mathematics series: American Mathematical Society, Providence, RI
    • Aitchison, J., 2002, Simplicial inference, in Viana, M. A. G., and Richards, D. S. P., eds., Algebraic methods in statistics and probability, v. 287, Contemporary mathematics series: American Mathematical Society, Providence, RI, p. 1-22.
    • (2002) Algebraic Methods in Statistics and Probability , vol.287 , pp. 1-22
    • Aitchison, J.1
  • 14
    • 33646245850 scopus 로고    scopus 로고
    • Compositional data analysis: Where are we and where should we be heading?
    • See Thió-Henestrosa and Martín-Fernández (2003) (electronic publication)
    • Aitchison, J., 2003, Compositional data analysis: Where are we and where should we be heading? See Thió-Henestrosa and Martín-Fernández (2003) (electronic publication).
    • (2003)
    • Aitchison, J.1
  • 15
    • 0004437577 scopus 로고    scopus 로고
    • Convex linear combination of compositions
    • Aitchison, J., and Bacon-Shone, J., 1999, Convex linear combination of compositions: Biometrika, v. 86, no. 2, p. 351-364.
    • (1999) Biometrika , vol.86 , Issue.2 , pp. 351-364
    • Aitchison, J.1    Bacon-Shone, J.2
  • 16
    • 4344677320 scopus 로고    scopus 로고
    • Compositional processes: A statistical search for understanding
    • See Bayer, Burger, and Skala 2002
    • Aitchison, J., Barceló-Vidal, C., 2002, Compositional processes: A statistical search for understanding: See Bayer, Burger, and Skala (2002, p. 381-386).
    • (2002) , pp. 381-386
    • Aitchison, J.1    Barceló-Vidal, C.2
  • 17
    • 21044435687 scopus 로고    scopus 로고
    • A concise guide for the algebraic-geometric structure of the simplex, the sample space for compositional data analysis
    • See Bayer, Burger, and Skala 2002
    • Aitchison, J., Barceló-Vidal, C., Egozcue, J. J., and Pawlowsky-Glahn, V., 2002, A concise guide for the algebraic-geometric structure of the simplex, the sample space for compositional data analysis. See Bayer, Burger, and Skala (2002, p. 387-392).
    • (2002) , pp. 387-392
    • Aitchison, J.1    Barceló-Vidal, C.2    Egozcue, J.J.3    Pawlowsky-Glahn, V.4
  • 19
    • 33646257723 scopus 로고    scopus 로고
    • Possible solution of some essential zero problems in compositional data analysis
    • See Thió-Henestrosa and Martín-Fernández (2003) (electronic publication)
    • Aitchison, J., and Kay, J., 2003, Possible solution of some essential zero problems in compositional data analysis. See Thió-Henestrosa and Martín-Fernández (2003) (electronic publication).
    • (2003)
    • Aitchison, J.1    Kay, J.2
  • 20
    • 0022195564 scopus 로고
    • Kernel density estimation for compositional data
    • Aitchison, J., and Lauder, I. J., 1985, Kernel density estimation for compositional data: J. R. Stat. Soc., Ser. C (Appl. Stat.), v. 34, no. 2, p. 129-137.
    • (1985) J. R. Stat. Soc. Ser. C (Appl. Stat.) , vol.34 , Issue.2 , pp. 129-137
    • Aitchison, J.1    Lauder, I.J.2
  • 21
    • 4344629393 scopus 로고    scopus 로고
    • Characterization of distributional forms for compositional data and associated distributional tests
    • Aitchison, J., Mateu-Figueras, G., and Ng, K. W., 2004, Characterization of distributional forms for compositional data and associated distributional tests: Math. Geol., v. 35, no. 6, p. 667-680.
    • (2004) Math. Geol. , vol.35 , Issue.6 , pp. 667-680
    • Aitchison, J.1    Mateu-Figueras, G.2    Ng, K.W.3
  • 22
    • 33646248577 scopus 로고    scopus 로고
    • Compositional hypotheses of subcompositional stability and specific perturbation change and their testing
    • See Thió-Henestrosa and Martín-Fernández (2003) (electronic publication)
    • Aitchison, J., and Ng, K. W., 2003, Compositional hypotheses of subcompositional stability and specific perturbation change and their testing. See Thió-Henestrosa and Martín-Fernández (2003) (electronic publication).
    • (2003)
    • Aitchison, J.1    Ng, K.W.2
  • 23
    • 0000764531 scopus 로고
    • Logistic-normal distributions. Some properties and uses
    • Aitchison, J., and Shen, S. M., 1980, Logistic-normal distributions. Some properties and uses: Biometrika, v. 67, no. 2, p. 261-272.
    • (1980) Biometrika , vol.67 , Issue.2 , pp. 261-272
    • Aitchison, J.1    Shen, S.M.2
  • 24
    • 0345510126 scopus 로고    scopus 로고
    • Differential perturbation processes: A tool for the study of compositional processes
    • See Buccianti, Nardi, and Potenza 1998
    • Aitchison, J., and Thomas, C. W., 1998, Differential perturbation processes: A tool for the study of compositional processes. See Buccianti, Nardi, and Potenza (1998, p. 499-504).
    • (1998) , pp. 499-504
    • Aitchison, J.1    Thomas, C.W.2
  • 25
    • 0001122047 scopus 로고    scopus 로고
    • Statistical applications of the multivariate skew-normal distribution
    • Azzalini, A., and Capitanio, A., 1999, Statistical applications of the multivariate skew-normal distribution: J. R. Stat. Soc., Ser. B (Stat. Methodol.) v. 61, no. 3, p. 579-602.
    • (1999) J. R. Stat. Soc. Ser. B (Stat. Methodol.) , vol.61 , Issue.3 , pp. 579-602
    • Azzalini, A.1    Capitanio, A.2
  • 26
    • 0001417140 scopus 로고    scopus 로고
    • The multivariate skew-normal distribution
    • Azzalini, A., and Dalla Valle, A., 1996, The multivariate skew-normal distribution: Biometrika, v. 83, no. 4, p. 715-726.
    • (1996) Biometrika , vol.83 , Issue.4 , pp. 715-726
    • Azzalini, A.1    Dalla Valle, A.2
  • 27
    • 0343701242 scopus 로고
    • Ranking methods for compositional data
    • Bacon-Shone, J., 1992, Ranking methods for compositional data: Appl. Stat., v. 41, no. 3, p. 533-537.
    • (1992) Appl. Stat. , vol.41 , Issue.3 , pp. 533-537
    • Bacon-Shone, J.1
  • 28
    • 33646266438 scopus 로고    scopus 로고
    • Modelling structural zeros in compositional data
    • See Thió-Henestrosa and Martín-Fernández (2003) (electronic publication)
    • Bacon-Shone, J., 2003, Modelling structural zeros in compositional data. See Thió-Henestrosa and Martín-Fernández (2003) (electronic publication).
    • (2003)
    • Bacon-Shone, J.1
  • 29
    • 0030455321 scopus 로고    scopus 로고
    • Some aspects of transformations of compositional data and the identification of outliers
    • Barceló, C., Pawlowsky-Glahn, V., and Grunsky, E., 1996, Some aspects of transformations of compositional data and the identification of outliers: Math. Geol., v. 28, no. 4, p. 501-518.
    • (1996) Math. Geol. , vol.28 , Issue.4 , pp. 501-518
    • Barceló, C.1    Pawlowsky-Glahn, V.2    Grunsky, E.3
  • 32
    • 0005954314 scopus 로고    scopus 로고
    • Statistical analysis and interpretation of discrete compositional data
    • NRCSE technical report 11: University of Washington, Seattle, Washington
    • Billheimer, D., Guttorp, P., and Fagan, W., 1997, Statistical analysis and interpretation of discrete compositional data: Technical report, NRCSE technical report 11: University of Washington, Seattle, Washington, 48 p.
    • (1997) Technical Report , pp. 48
    • Billheimer, D.1    Guttorp, P.2    Fagan, W.3
  • 33
    • 1542679362 scopus 로고    scopus 로고
    • Statistical interpretation of species composition
    • Billheimer, D., Guttorp, P., and Fagan, W., 2001, Statistical interpretation of species composition: J. Am. Stat. Assoc., v. 96, no. 456, p. 1205-1214.
    • (2001) J. Am. Stat. Assoc. , vol.96 , Issue.456 , pp. 1205-1214
    • Billheimer, D.1    Guttorp, P.2    Fagan, W.3
  • 36
    • 33646231950 scopus 로고    scopus 로고
    • Random variables and geochemical processes: A way to describe natural variability
    • Ottonello, G., and Serva, L., Geochemical baselines of Italy, Chapter 4: Pacini Editore, Genova, Italy
    • Buccianti, A., and Pawlowsky-Glahn, V., 2003, Random variables and geochemical processes: A way to dIscribe natural variability: in Ottonello, G., and Serva, L., Geochemical baselines of Italy, Chapter 4: Pacini Editore, Genova, Italy, 294 p.
    • (2003) , pp. 294
    • Buccianti, A.1    Pawlowsky-Glahn, V.2
  • 37
    • 0007275271 scopus 로고    scopus 로고
    • Visualization and modeling of natural trends in ternary diagrams
    • See Lippard, Næss, and Sinding-Larsen 1999
    • Buccianti, A., Pawlowsky-Glahn, V., Barceló-Vidal, C., and Jarauta-Bragulat, E., 1999, Visualization and modeling of natural trends in ternary diagrams: A geochemical case study. See Lippard, Næss, and Sinding-Larsen (1999, p. 139-144).
    • (1999) A Geochemical Case Study , pp. 139-144
    • Buccianti, A.1    Pawlowsky-Glahn, V.2    Barceló-Vidal, C.3    Jarauta-Bragulat, E.4
  • 38
    • 33646245384 scopus 로고    scopus 로고
    • New insights on river water chemistry by using noncentred simplicial principal component analysis: A case study
    • See Thió-Henestrosa and Martín-Fernández (2003) (electronic publication)
    • Buccianti, A., Vaselli, O., and Nisi, B., 2003, New insights on river water chemistry by using noncentred simplicial principal component analysis: A case study. See Thió-Henestrosa and Martín-Fernández (2003) (electronic publication).
    • (2003)
    • Buccianti, A.1    Vaselli, O.2    Nisi, B.3
  • 39
    • 0002920322 scopus 로고
    • The effects of closure on the moments of a distribution
    • Butler, J. C., 1979, The effects of closure on the moments of a distribution: Math. Geol., v. 11, no. 1, p. 75-84.
    • (1979) Math. Geol. , vol.11 , Issue.1 , pp. 75-84
    • Butler, J.C.1
  • 40
    • 0000429235 scopus 로고
    • On correlation between variables of constant sum
    • Chayes, F., 1960, On correlation between variables of constant sum: J. Geophys. Res., v. 65, no. 12, p. 4185-4193.
    • (1960) J. Geophys. Res. , vol.65 , Issue.12 , pp. 4185-4193
    • Chayes, F.1
  • 41
    • 33646257260 scopus 로고    scopus 로고
    • Least squares regression in the simplex
    • See Bayer, Burger, and Skala 2002
    • Daunis-i-Estadella, J., Egozcue, J. J., and Pawlowsky-Glahn, V., 2002, Least squares regression in the simplex. See Bayer, Burger, and Skala (2002, p. 411-416).
    • (2002) , pp. 411-416
    • Daunis-i-Estadella, J.1    Egozcue, J.J.2    Pawlowsky-Glahn, V.3
  • 42
    • 33646244766 scopus 로고    scopus 로고
    • Groups of parts and their balances in compositional data analysis
    • Egozcue, J. J., and Pawlowsky-Glahn, V., 2005, Groups of parts and their balances in compositional data analysis. Math. Geol., v. 37, no. 7, p. 795-828.
    • (2005) Math. Geol. , vol.37 , Issue.7 , pp. 795-828
    • Egozcue, J.J.1    Pawlowsky-Glahn, V.2
  • 43
  • 44
    • 0034094942 scopus 로고    scopus 로고
    • Compositional data analysis and zeros in micro data
    • Fry, J. M., Fry, T. R. L., and McLaren, K. R., 2000, Compositional data analysis and zeros in micro data: Appl. Econ., v. 32, no. 8, p. 953-959.
    • (2000) Appl. Econ. , vol.32 , Issue.8 , pp. 953-959
    • Fry, J.M.1    Fry, T.R.L.2    McLaren, K.R.3
  • 45
    • 77956887176 scopus 로고
    • The biplot - Graphic display of matrices with application to principal component analysis
    • Gabriel, K. R., 1971, The biplot - graphic display of matrices with application to principal component analysis: Biometrika, v. 58, no. 3, p. 453-467.
    • (1971) Biometrika , vol.58 , Issue.3 , pp. 453-467
    • Gabriel, K.R.1
  • 46
    • 0002379614 scopus 로고
    • Biplot display of multivariate matrices for inspection of data and diagnosis
    • Barnett, V., ed. Wiley, New York
    • Gabriel, K. R., 1981, Biplot display of multivariate matrices for inspection of data and diagnosis, in Barnett, V., ed., Interpreting multivariate data: Wiley, New York, p. 147-173.
    • (1981) Interpreting Multivariate Data , pp. 147-173
    • Gabriel, K.R.1
  • 47
    • 0000029482 scopus 로고
    • The geometric mean, in vital and social statistics
    • Galton, F., 1879, The geometric mean, in vital and social statistics: Proc. R. Soc. Lond., v. 29, p. 365-366.
    • (1879) Proc. R. Soc. Lond. , vol.29 , pp. 365-366
    • Galton, F.1
  • 50
    • 0000025263 scopus 로고    scopus 로고
    • A measure of difference for compositional data based on measures of divergence
    • See Lippard, Næss, and Sinding-Larsen 1999
    • Martín-Fernández, J. A., Bren, M., Barceló-Vidal, C., and Pawlowsky-Glahn, V., 1999, A measure of difference for compositional data based on measures of divergence. See Lippard, Næss, and Sinding-Larsen (1999, p. 211-216).
    • (1999) , pp. 211-216
    • Martín-Fernández, J.A.1    Bren, M.2    Barceló-Vidal, C.3    Pawlowsky-Glahn, V.4
  • 51
    • 33646240299 scopus 로고    scopus 로고
    • Markov chain Monte Carlo method applied to rounding zeros of compositional data: First approach
    • See Thió-Henestrosa and Martín-Fernández (2003) (electronic publication)
    • Martin-Fernández, J. A., Paladea-Albadalejo, J., and Gómez-García, J., 2003, Markov chain Monte Carlo method applied to rounding zeros of compositional data: First approach. See Thió-Henestrosa and Martín-Fernández (2003) (electronic publication).
    • (2003)
    • Martin-Fernández, J.A.1    Paladea-Albadalejo, J.2    Gómez-García, J.3
  • 52
    • 4344571560 scopus 로고    scopus 로고
    • Models de distribució sobre el símplex
    • PhD Thesis, Universitat Politècnica de Catalunya, Barcelona, Spain
    • Mateu-Figueras, G., 2003, Models de distribució sobre el símplex: PhD Thesis, Universitat Politècnica de Catalunya, Barcelona, Spain.
    • (2003)
    • Mateu-Figueras, G.1
  • 53
    • 0742273799 scopus 로고    scopus 로고
    • Modeling compositional data with multivariate skew-normal distributions
    • See Buccianti, Nardi, and Potenza 1998
    • Mateu-Figueras, G., Barceló-Vidal, C., and Pawlowsky-Glahn, V., 1998, Modeling compositional data with multivariate skew-normal distributions. See Buccianti, Nardi, and Potenza (1998, p. 532-537).
    • (1998) , pp. 532-537
    • Mateu-Figueras, G.1    Barceló-Vidal, C.2    Pawlowsky-Glahn, V.3
  • 54
    • 33646266682 scopus 로고    scopus 로고
    • Una alternativa a la distribución lognormal
    • See Saralegui and Ripoll (2003) (electronic publication)
    • Mateu-Figueras, G., and Pawlowsky-Glahn, V., 2003, Una alternativa a la distribución lognormal. See Saralegui and Ripoll (2003) (electronic publication).
    • (2003)
    • Mateu-Figueras, G.1    Pawlowsky-Glahn, V.2
  • 56
    • 0000216454 scopus 로고
    • The law of the geometric mean
    • McAlister, D., 1879, The law of the geometric mean: Proc. R. Soc. Lond., v. 29, p. 367-376.
    • (1879) Proc. R. Soc. Lond. , vol.29 , pp. 367-376
    • McAlister, D.1
  • 57
    • 0002567040 scopus 로고
    • On the compound multinomial distribution, the multivariate β-distribution and correlations among proportions
    • Mosimann, J. E., 1962, On the compound multinomial distribution, the multivariate β-distribution and correlations among proportions: Biometrika, v. 49, nos. 1-2, p. 65-82.
    • (1962) Biometrika , vol.49 , Issue.1-2 , pp. 65-82
    • Mosimann, J.E.1
  • 58
    • 33646237075 scopus 로고    scopus 로고
    • Statistical modelling on coordinates
    • See (Thió-Henestrosa and Martín-Fernández, 2003) (electronic publication)
    • Pawlowsky-Glahn, V., 2003, Statistical modelling on coordinates. See (Thió-Henestrosa and Martín-Fernández, 2003) (electronic publication).
    • (2003)
    • Pawlowsky-Glahn, V.1
  • 59
    • 0036204483 scopus 로고    scopus 로고
    • Visualization and modeling of subpopulations of compositional data: Statistical methods illustrated by means of geochemical data from fumarolic fluids
    • Pawlowsky-Glahn, V., and Buccianti, A., 2002, Visualization and modeling of subpopulations of compositional data: Statistical methods illustrated by means of geochemical data from fumarolic fluids: Int. J. Earth Sci. (Geol. Rundschau), v. 91, no. 2, p. 357-368.
    • (2002) Int. J. Earth Sci. (Geol. Rundschau) , vol.91 , Issue.2 , pp. 357-368
    • Pawlowsky-Glahn, V.1    Buccianti, A.2
  • 61
    • 0037912028 scopus 로고    scopus 로고
    • BLU estimators and compositional data
    • Pawlowsky-Glahn, V., and Egozcue, J. J., 2002, BLU estimators and compositional data: Math. Geol., v. 34, no. 3, p. 259-274.
    • (2002) Math. Geol. , vol.34 , Issue.3 , pp. 259-274
    • Pawlowsky-Glahn, V.1    Egozcue, J.J.2
  • 63
    • 0000629281 scopus 로고
    • Mathematical contributions to the theory of evolution. On a form of spurious correlation which may arise when indices are used in the measurement of organs
    • Pearson, K., 1897, Mathematical contributions to the theory of evolution. On a form of spurious correlation which may arise when indices are used in the measurement of organs: Proc. R. Soc. Lond., v. LX, p. 489-502.
    • (1897) Proc. R. Soc. Lond. , vol.60 , pp. 489-502
    • Pearson, K.1
  • 64
    • 21144462522 scopus 로고
    • The resolution of a compositional data set into mixtures of fixed source components
    • Renner, R. M., 1993, The resolution of a compositional data set into mixtures of fixed source components: J. R. Stat. Soc., Ser. C (Appl. Stat.), v. 42, no. 4, p. 615-631.
    • (1993) J. R. Stat. Soc. Ser. C (Appl. Stat.) , vol.42 , Issue.4 , pp. 615-631
    • Renner, R.M.1
  • 65
    • 33646259915 scopus 로고    scopus 로고
    • Actas del XXVII Congreso Nacional de la Sociedad de Estadística e Investigación Operativa (SEIO)
    • eds. CD-ROM: Sociedad de Estadística e Investigación Operativa, Lleida (Spain)
    • Saralegui J., and Ripoll, E., eds., 2003, Actas del XXVII Congreso Nacional de la Sociedad de Estadística e Investigación Operativa (SEIO), CD-ROM: Sociedad de Estadística e Investigación Operativa, Lleida (Spain).
    • (2003)
    • Saralegui, J.1    Ripoll, E.2
  • 67
    • 33646269677 scopus 로고    scopus 로고
    • Compositional Data Analysis Workshop - CoDaWork'03
    • eds. Proceedings: Universitat de Girona, CD-ROM, ISBN 84-8458-111-X available at
    • Thió-Henestrosa, S., and Martín-Fernández, J. A., eds., 2003, Compositional Data Analysis Workshop - CoDaWork'03, Proceedings: Universitat de Girona, CD-ROM, ISBN 84-8458-111-X, available at http://ima.udg.es/Activitats/CoDaWork03/.
    • (2003)
    • Thió-Henestrosa, S.1    Martín-Fernández, J.A.2
  • 68
    • 4344634734 scopus 로고    scopus 로고
    • The use of logratios in subcompositional analysis and geochemical discrimination of metamorphosed limestones from the northeast and central scottish highlands
    • See Buccianti, Nardi, and Potenza 1998
    • Thomas, C. W., and Aitchison, J., 1998, The use of logratios in subcompositional analysis and geochemical discrimination of metamorphosed limestones from the northeast and central scottish highlands. See Buccianti, Nardi, and Potenza (1998, p. 549-554).
    • (1998) , pp. 549-554
    • Thomas, C.W.1    Aitchison, J.2
  • 69
    • 33646245624 scopus 로고    scopus 로고
    • Exploration of geological variability and possible processes through the use of compositional data analysis: An example using Scottish metamorphosed limestones
    • See Buccianti, Nardi, and Potenza (1998) (electronic publication)
    • Thomas, C. W., and Aitchison, J., 2003, Exploration of geological variability and possible processes through the use of compositional data analysis: An example using Scottish metamorphosed limestones. See Buccianti, Nardi, and Potenza (1998) (electronic publication).
    • (2003)
    • Thomas, C.W.1    Aitchison, J.2
  • 70
    • 33646233459 scopus 로고    scopus 로고
    • Extracting latent factor subcompositions from hydrochemical conpositions
    • Tolosana-Delgado, R., Otero, N., Pawlowsky-Glahn, V., and Soler, A., 2005, Extracting latent factor subcompositions from hydrochemical conpositions. Math. Geol., v. 37, no. 7, p. 681-702.
    • (2005) Math. Geol. , vol.37 , Issue.7 , pp. 681-702
    • Tolosana-Delgado, R.1    Otero, N.2    Pawlowsky-Glahn, V.3    Soler, A.4
  • 73
    • 0742323445 scopus 로고    scopus 로고
    • Modelling compositional change: The example of chemical weathering of granitoid rocks
    • von Eynatten, H., Barceló-Vidal, C., and Pawlowsky-Glahn, V., 2003, Modelling compositional change: The example of chemical weathering of granitoid rocks Math. Geol. v. 35 no. 3 p. 231-251.
    • (2003) Math. Geol , vol.35 , Issue.3 , pp. 231-251
    • von Eynatten, H.1    Barceló-Vidal, C.2    Pawlowsky-Glahn, V.3
  • 74
    • 0742325558 scopus 로고    scopus 로고
    • Understanding perturbation on the simplex: A simple method to better visualize and interpret compositional data in ternary diagrams
    • von Eynatten, H., Pawlowsky-Glahn, V., and Egozcue, J. J., 2002, Understanding perturbation on the simplex: A simple method to better visualize and interpret compositional data in ternary diagrams: Math. Geol., v. 34, no. 3, p. 249-257.
    • (2002) Math. Geol. , vol.34 , Issue.3 , pp. 249-257
    • von Eynatten, H.1    Pawlowsky-Glahn, V.2    Egozcue, J.J.3
  • 75
    • 0031450970 scopus 로고    scopus 로고
    • End-member modeling of compositional data: Numerical-statistical algorithms for solving the explicit mixing problem
    • Weltje, J. G., 1997, End-member modeling of compositional data: Numerical-statistical algorithms for solving the explicit mixing problem: Math. Geol., v. 29, no. 4, p. 503-549.
    • (1997) Math. Geol. , vol.29 , Issue.4 , pp. 503-549
    • Weltje, J.G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.