Groups of Parts and Their Balances in Compositional Data Analysis

By Juan José Egozcue, Vera Pawlowsky-Glahn. 2005

641 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Geophysics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/eb93c8aaaee240122b354f10b26c6bf550fa5991

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Citations in the corpus

On the Interpretation of Orthonormal Coordinates for Compositional Data (2011, methodology): “In addition, the possibility of expressing compositional data in real space by using log-ratio transformations (Aitchison 1986) was proposed, in particular as coordinates with respect to an orthonormal basis on the simplex (Egozcue et al. 2003; Egozcue and Pawlowsky-Glahn 2005).”
Imputation of missing values for compositional data using classical and robust methods (2010, methodology): “The ilr transformation results in a D − 1 dimensional real space, and it offers good theoretical and practical properties (Egozcue and Pawlowsky-Glahn, 2005).”
The mathematics of compositional analysis (2016, positive): “Egozcue and Pawlowsky-Glahn (2005) describe a stepwise procedure to make an orthonormal basis of CD from sequential binary partitions of components of the observational vectors of IR+ .”
Exploring Compositional Data with the CoDa-Dendrogram (2011, methodology): “A useful way to build up an orthonormal basis of the simplex whose coordinates may be easily interpretable is to define a sequential binary partition (SBP) of the compositional vector.”
Systematic comparison of five machine-learning models in classification and interpolation of soil particle size fractions using different transformed data (2020, methodology): “Table S3 All choices of SBP of soil PSF data (D = 3), the orders of soil PSF data are (𝑠𝑎𝑛𝑑, 𝑠𝑖𝑙𝑡, 𝑐𝑙𝑎𝑦), (𝑠𝑖𝑙𝑡, 𝑐𝑙𝑎𝑦, 𝑠𝑎𝑛𝑑) and (𝑐𝑙𝑎𝑦, 𝑠𝑎𝑛𝑑, 𝑠𝑖𝑙𝑡).”
On the interpretation of differences between groups for compositional data (2015, positive): “Following Egozcue and Pawlowsky-Glahn (2005) one can define a particular ilr coordinates created through a sequential binary partition (SPB).”
Bayes Hilbert Spaces (2014, neutral): “These Fourier coefficients are called balances (Egozcue & Pawlowsky-Glahn 2005), and they are explicitly equal to ci(1)=〈fi, e1〉B2(P) = 1√ 2 log fi(1) fi(2) , ci(2)=〈fi, e2〉B2(P) = √ 2√ 3 log (fi(1)fi(2))1=2 (fi(3)) .”
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.”
Compositional data: the sample space and its structure (2019, methodology): “As described in Aitchison and Egozcue (2005), CoDa analyses in which the relevant functions of the composition are scale-invariant guarantee subcompositional coherence.”
Correlation Analysis for Compositional Data (2009, background): “[7] Egozcue JJ, Pawlowsky-Glahn V (2005) Groups of parts and their balances in compositional data analysis.”
Aitchison’s Compositional Data Analysis 40 Years on: A Reappraisal (2022, methodology): “Whereas the set of D CLRs is indeed isometric, the isometric logratio (ILR) transformation was introduced into CoDA [20] specifically to obtain a set of d logratios, the dimensionality of the data, that were both linearly independent and isometric.”
ANOVA-Like Differential Expression (ALDEx) Analysis for Mixed Population RNA-Seq (2013, methodology): “showed that this space of log-proportions was equivalent to a Euclidean vector space[17,18] and as such, contributions from the subspace spanning 1⁄21,1 , here termed the ’’uninformative subspace,’’ can be removed via standard techniques from linear algebra.”
Linear regression with compositional explanatory variables (2012, background): “Naturally, there are several ways to construct such a basis, and in the context of compositional data this can be done with a method called sequential binary partitioning [8].”