Biplots of Compositional Data

By J. Aitchison, Michael J. Greenacre. 2002

699 citations recorded by the source corpus.

Subfields: Archeology, Artificial Intelligence, Geochemistry and Petrology

View Paper: https://www.semanticscholar.org/paper/688fcd026b80cb7221f3c28e2b0ba5459644d74d

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Citations in the corpus

On the use of archetypes as benchmarks (2008, neutral): “Hence, suitable methods developed for their analysis can be exploited to gain further insights into the data structure [39, 40].”
Exploring Compositional Data with the CoDa-Dendrogram (2011, methodology): “Two exploratory tools are very helpful for this purpose: (a) the variation array (Aitchison, 1986), shown in Figure 2; and (b), the biplot (Aitchison and Greenacre, 2002), shown in Figure 3 jointly for eastern and western countries.”
A Novel Sparse Compositional Technique Reveals Microbial Perturbations (2019, methodology): “Fortunately, feature loadings can be extracted from RPCA while utilizing the same interpretation as suggested in the work of Aitchison and Greenacre (25).”
Simple Correspondence Analysis: A Bibliographic Review (2004, background): “These co-ordinates were also described in Aitchison & Greenacre (2002).”
Compositional Data Analysis: Where Are We and Where Should We Be Heading? (2005, methodology): “For details of biplot construction see Aitchison (1990b, 1997, 2001) and Aitchison and Greenacre (2002) .”
Compositional Data Analysis of Some Alkaline Glasses (2005, background): “Figure 2 shows the outcome of PCAs of the data, presented as biplots ( Aitchison and Greenacre, 2002 ), where the emphasis is on representing the relationship between rows of the data matrix rather than the covariance structure of the variables.”
On the interpretation of differences between groups for compositional data (2015, methodology): “Aitchison and Greenacre (2002) adapted the typical biplot for CoDa and in doing so introduced the clr-biplot, that is, the biplot of clr coordinates.”
Aitchison’s Compositional Data Analysis 40 Years on: A Reappraisal (2022, methodology): “The PCA of the CLRs, which is equivalent to the PCA of all the LRs, is a special case where both the CLRs and their difference vectors are optimally displayed [7].”
Dealing with Zeros and Missing Values in Compositional Data Sets Using Nonparametric Imputation (2003, methodology): “Following P1: GCR Mathematical Geology [mg] pp851-matg-465362 May 15, 2003 1:4 Style file version June 25th, 2002 Dealing With Zeros and Missing Values in Compositional Data Sets 265 Aitchison and Greenacre (2002), the data set can be represented in a biplot diagram (Fig.”
An R package for statistical provenance analysis (2016, methodology): “Thus, the PCA biplot facilitates the interpretation of the configuration in terms of underlying processes (Aitchison and Greenacre, 2002).”
Correspondence analysis (2010, background): “Standard row coordinates: = D−2 r U (5) Standard column coordinates: = D−2 c V.”
Microbiome Datasets Are Compositional: And This Is Not Optional (2017, methodology): “It is possible to glean substantial qualitative information regarding the quality of the dataset and the relationships between groups with this tool (Aitchison and Greenacre, 2002; Gloor et al., 2016b), and examples are shown in the “Biplot” section of the Supplement.”