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Power transformations in correspondence analysis
Greenacre, Michael
Universitat Pompeu Fabra. Departament d'Economia i Empresa
Power transformations of positive data tables, prior to applying the correspondence analysis algorithm, are shown to open up a family of methods with direct connections to the analysis of log-ratios. Two variations of this idea are illustrated. The first approach is simply to power the original data and perform a correspondence analysis this method is shown to converge to unweighted log-ratio analysis as the power parameter tends to zero. The second approach is to apply the power transformation to thecontingency ratios, that is the values in the table relative to expected values based on the marginals this method converges to weighted log-ratio analysis, or the spectral map. Two applications are described: first, a matrix of population genetic data which is inherently two-dimensional, and second, a larger cross-tabulation with higher dimensionality, from a linguistic analysis of several books.
Statistics, Econometrics and Quantitative Methods
box-cox transformation
chi-square distance
contingency ratio
correspondence analysis
log-ratio analysis
power transformation
ratio data
singular value decomposition
spectral map
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