Logratio Analysis and Compositional Distance

By J. Aitchison, C. Barceló‐Vidal, Josep-Antoni Martín-Fernández, Vera Pawlowsky-Glahn. 2000

509 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Mechanics of Materials, Media Technology

View Paper: https://www.semanticscholar.org/paper/39a5ab0d5f29e150ee6510a03f610f6ae44971d3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Mechanics of Materials

In Media Technology

Citations in the corpus

A data-based power transformation for compositional data (2011, background): “Over the years there has been a debate over whether it is preferable to use RDA or LRA (Barceló et al., 1996; Aitchison, 1999; Aitchison et al., 2000; Beardah et al., 2003; Sharp, 2006).”
Colours and Cocktails: Compositional Data Analysis 2013 Lancaster Lecture (2014, background): “A second exchange between Zier & Rehder (1998), Rehder & Zier (2001) and Aitchison et al. (2000), Aitchison, Barceló-Vidal and Pawlowsky-Glahn (2001) clarified some issues but was less important because the key ideas had already been set out.”
Linear regression with compositional explanatory variables (2012, background): “Keywords: mixtures;Aitchison geometry on the simplex; isometric logratio transformation; orthonormal coordinates”
On the use of archetypes as benchmarks (2008, unknown): “In this direction, it may be worth to investigate ways to assign performers to different clusters based on their proximity to the archetypes, bearing in mind that the definition of distance measures for compositional data is still an open issue [41, 42].”
Imputation of missing values for compositional data using classical and robust methods (2010, background): “A distance measure that is accounting for this relative scale property is the Aitchison distance (Aitchison et al., 2000) , defined for two compositions x = (x 1 , . . . , x D ) t and y = (y 1 , . . . , y D ) t as d A (x, y) = 1 D D−1 i=1 D j=i+1 ln x i x j − ln y i y j 2 .”
A Parametric Approach for Dealing with Compositional Rounded Zeros (2007, methodology): “The alr transformation is not isometric, consequently these measures could show a different pattern if they are computed on the alr-transformed space using the Euclidean distance ( Aitchison et al. 2000 ).”
Microbiome Datasets Are Compositional: And This Is Not Optional (2017, methodology): “Distances between features are non-linear when examined from a Euclidian perspective (Martín-Fernández et al., 1998; Aitchison et al., 2000) and many DD matrices are used that partially address this problem.”