Principal component analysis of compositional data

Aitchison, J.

doi:10.1093/biomet/70.1.57

Cited by 456 publications

(250 citation statements)

References 18 publications

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“…In particular, because of inherent curvature in proportional data, the property of zero correlations between eigenvectors is questionable and the constant sum constraint leads to a bias towards negative correlations among the raw proportions. To mitigate these problems, we used a log-linear contrast proposed by Aitchison (1983), in which the vector of proportions (x) is replaced by a vector given by log[x\g(x)], where…”

Section: Statistical Proceduresmentioning

confidence: 99%

Evolutionary divergence in the pan‐Atlantic mangrove Avicennia germinans

Dodd¹,

Rafii²,

Bousquet-Mélou³

2000

New Phytologist

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Cuticular hydrocarbon composition was determined for 18 populations of Avicennia germinans (Avicenniaceae) collected from West Africa, Florida, the Pacific coast of Mexico and French Guyana. Variation in covariance structure among the hydrocarbons was evaluated from correlations among the traits for each of the populations and from a hierarchical common principal components analysis. Principal components ordinations of populations based on the 171 z* transformed correlation coefficients, onto which a minimal spanning tree was superimposed, suggested a network in which French Guyanan populations formed a nexus from which African populations differentiated biochemically from Floridan and Mexican groups. Common principal components analysis provided further support for the differentiation in covariance structure among these biochemical traits of African populations. Pacific coast Mexican populations appeared to have diverged less in covariation among traits from Atlantic American sources than did the northern (Floridan) and southern (French Guyanan) Atlantic American populations from one another. The complete isolation of Pacific coast sources after emergence of the Central American isthmus during the Pliocene provides a reference for comparison of levels of differentiation among regions that suggests an underlying pattern of divergence in this species. Partial Mantel matrix tests revealed significant geographic effects, with no significant climatic effects. Our results provide support for recognition of a major differentiation between Old and New World sources within the taxon and indicate the need for a full revision of this species.

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Section: Statistical Proceduresmentioning

confidence: 99%

Evolutionary divergence in the pan‐Atlantic mangrove Avicennia germinans

Dodd¹,

Rafii²,

Bousquet-Mélou³

2000

New Phytologist

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“…showed that principal component analysis recovers exactly the parameters of equal tolerance Gaussian curves and surfaces from error-free data when the data matrix is centered by rows and by columns after log transformation. Aitchison (1983) proposed this transformation to overcome the difficulty of the constant-sum constraint in principal component analysis of compositional data. He notices that "the nonlinearity of the logarithmic function opens up the possibility of coping with curvature in data sets ...," but does not refer to the Gaussian or unimodal response model.…”

Section: Discussionmentioning

confidence: 99%

Unimodal Models to Relate Species to Environment.

Braak¹

1988

Biometrics

124

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“…Principal component analysis of compositional data (Aitchison 1983) and the corresponding biplots (Aitchison and Greenacre 2002) are powerful tools for exploring compositional data. This is also the case in exploring microbiome data (Gloor et al 2016).…”

Section: Example Using An 16s Rrna Gene Profiling Casementioning

confidence: 99%

Linear Association in Compositional Data Analysis

Egozcue

Pawlowsky‐Glahn²,

Gloor³

2018

AJS

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With compositional data, ordinary covariation indices, designed for real random variables, fail to describe dependence. There is a need for compositional alternatives to covariance and correlation. Based on the Euclidean structure of the simplex, called Aitchison geometry, compositional association is identified to a linear restriction of the sample space when a log-contrast is constant. In order to simplify interpretation, a sparse and simple version of compositional association is defined in terms of balances which are constant across the sample. It is called b-association. This kind of association of compositional variables is extended to association between groups of compositional variables. In practice, exact b-association seldom occurs, and measures of degree of b-association are reviewed based on those previously proposed. Also, some techniques for testing b-association are studied. These techniques are applied to available oral microbiome data to illustrate both their advantages and difficulties. Both testing and measurements of b-association appear to be quite sensitive to heterogeneities in the studied populations and to outliers.

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Principal component analysis of compositional data

Cited by 456 publications

References 18 publications

Evolutionary divergence in the pan‐Atlantic mangrove Avicennia germinans

Evolutionary divergence in the pan‐Atlantic mangrove Avicennia germinans

Unimodal Models to Relate Species to Environment.

Linear Association in Compositional Data Analysis

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