Tsagris, Michail and Preston, Simon and T.A. Wood, Andrew (2016): Improved classi cation for compositional data using the $\alpha$transformation. Forthcoming in: Journal of Classification (2016)

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Abstract
In compositional data analysis an observation is a vector containing nonnegative values, only the relative sizes of which are considered to be of interest. Without loss of generality, a compositional vector can be taken to be a vector of proportions that sum to one. Data of this type arise in many areas including geology, archaeology, biology, economics and political science. In this paper we investigate methods for classi�cation of compositional data. Our approach centres on the idea of using the �transformation to transform the data and then to classify the transformed data via regularised discriminant analysis and the knearest neighbours algorithm. Using the �transformation generalises two rival approaches in compositional data analysis, one (when α=1) that treats the data as though they were Euclidean, ignoring the compositional constraint, and another (when $\alpha$ = 0) that employs Aitchison's centred logratio transformation. A numerical study with several real datasets shows that whether using $\alpha$ = 1 or $\alpha$ = 0 gives better classification performance depends on the dataset, and moreover that using an intermediate value of α can sometimes give better performance than using either 1 or 0.
Item Type:  MPRA Paper 

Original Title:  Improved classi cation for compositional data using the $\alpha$transformation 
Language:  English 
Keywords:  compositional data, classi�cation, �transformation, �metric, JensenShannon divergence 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C18  Methodological Issues: General 
Item ID:  67657 
Depositing User:  Mr Michail Tsagris 
Date Deposited:  05. Nov 2015 14:57 
Last Modified:  05. Nov 2015 15:14 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/67657 