Geometric approach to statistical analysis on the simplex

By Vera Pawlowsky-Glahn, Juan José Egozcue. 2001

420 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/899e320122bf33360f01905da06070c4586e7c45

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In Artificial Intelligence

Citations in the corpus

"compositions": A unified R package to analyze compositional data (2008, methodology): “Apart from these classical statistics, the package contains also functions to compute several advanced spread measures defined in the scope of Aitchison’s approach to compositions: the variation and covariation matrices (Aitchison, 1986), and the metric variance, covariance and standard deviation (P”
Hilbert Space of Probability Density Functions Based on Aitchison Geometry (2006, background): “On the basis of an early work by Aitchison [1, 2], it was completed only recently, when the Aitchison distance in the simplex was associated with an inner product—leading to the recognition of a finite-dimensional Hilbert space structure [3, 4 , 5]—and orthonormal bases were identified [6].”
Exploring Compositional Data with the CoDa-Dendrogram (2011, background): “Keywords: Aitchison Geometry, Euclidean Vector Space, Orthonormal Coordinates.”
Isometric Logratio Transformations for Compositional Data Analysis (2003, methodology): “each component is divided by the sum of all the components and then multiplied by •, so that the resulting row vector is in S D ) (Aitchison, 2002; Billheimer, Guttorp, and Fagan, 2001; Pawlowsky-Glahn and Egozcue, 2001, 2002 ).”
Groups of Parts and Their Balances in Compositional Data Analysis (2005, background): “For further details see Aitchison (2003a), Aitchison and others (2002), Billheimer, Guttorp, and Fagan (2001), Egozcue and others (2003), and Pawlowsky-Glahn and Egozcue (2001).”
On the interpretation of differences between groups for compositional data (2015, background): “In practical terms, Pawlowsky-Glahn and Egozcue (2001) stated that the centre µ is the geometric mean of X, whose ilr coordinates ilr(µ) are, respectively, equal to the arithmetic mean of ilr(X).”
Tools for compositional data with a total (2015, methodology): “The operation ⊕+ is called plus-perturbation, by analogy to the group operation in the simplex, called perturbation (Aitchison, 1986, Chapter 2; Pawlowsky-Glahn and Egozcue, 2001).”
Dealing with Zeros and Missing Values in Compositional Data Sets Using Nonparametric Imputation (2003, background): “See Aitchison (2002), Billheimer, Guttorp, and Fagan (2001) and Pawlowsky-Glahn and Egozcue (2001, 2002) for further details.”
Bayes linear spaces (2010, methodology): “…Received: February 2010 Accepted: October 2010 group operation, and its Euclidean structure has been completed (Billheimeret al., 2001; Pawlowsky-Glahn and Egozcue, 2001, 2002; Egozcueet al., 2003) The extension of the underlying ideas to compositions of infinitely many parts is due…”
Bayes Hilbert Spaces (2014, methodology): “This idea was applied to define the metric centre and variance of random variables in R+ and in the simplex (Pawlowsky-Glahn & Egozcue 2001).”