Isometric Logratio Transformations for Compositional Data Analysis

By Juan José Egozcue, Vera Pawlowsky-Glahn, G. Mateu-Figueras, C. Barceló‐Vidal. 2003

1,866 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Geophysics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/a6a1d1517e2ccd59a798611bedf9266e5965137d

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Citations in the corpus

Principal component analysis for compositional data with outliers (2009, methodology): “Egozcue et al. (2003) suggested to use the basis v i = Clearly, another chosen orthonormal basis of H leads to orthogonal transformation of both the resulting data and the original data on the simplex (here in the sense of the corresponding simplicial, so called Aitchison inner product), see…”
Spatial Regression Modeling for Compositional Data With Many Zeros (2013, methodology): “Compositional data are therefore often analyzed using transformations such as the additive logratio (alr) transformation (Aitchison, 1986) or isometric logratio (ilr) transformation (Egozcue et al., 2003), whence standard multivariate methods can then be applied to the transformed data.”
Assessment of Various Fuzzy c-Mean Clustering Validation Indices for Mapping Mineral Prospectivity: Combination of Multifractal Geochemical Model and Mineralization Processes (2019, methodology): “Prior to statistical assessment and to remove the effects of skewed distributions and data closure on multivariate methods (Aitchison 1986; Afzal et al. 2011), the geochemical data were subjected to the isometric log ratio (ilr) transformation (Egozcue et al. 2003).”
Ipsative measurement and the analysis of organizational values: an alternative approach for data analysis (2014, methodology): “…either based on parametric statistical methods such as: (a) The closed geometric mean which is often used in geology (e.g., Aitchison 1982, 1986; Egozcue et al. 2003), or nonparametric methods such as: (b) The nonparametric bootstrap test (e.g., Efron and Tibshirani 1993), and: (c) The…”
Tools for compositional data with a total (2015, methodology): “A first inspection of the data, using a blind sequential binary partition (SBP) (Egozcue and Pawlowsky-Glahn, 2005) and the associated ilr transformation (Egozcue et al., 2003), shown in Figure 1, evidenced a different behaviour of the samples taken before (B) and after (A) January 1, 1998.”
Bayes Hilbert Spaces (2014, background): “The analysis of compositional data (Aitchison 1986) and its algebraic-geometric developments have revealed that the simplex has a meaningful Euclidean space structure (Billheimer, Guttorp & Fagan 2001; Egozcue et al. 2003; Pawlowsky-Glahn & Egozcue 2001).”
"compositions": A unified R package to analyze compositional data (2008, methodology): “Coordinates are computed using the ilr transformation (Egozcue et al., 2003) (see Tables 1–2 for their definitions), which also uses the Helmert matrix (Eq.”