Power Transformations in Correspondence Analysis
Speaker: Prof. Michael Greenacre, Universitat Pompeu Fabra, Barcelona
When: 2009-10-15 11:00:00
Venue: Queensland Brain Institute (building 79) Level 7 Auditorium
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Abstract: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 transform 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 the contingency 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. Various applications are described, in the context of genetics,
linguistics and compositional data in chemistry, and dynamic graphics is
used to demonstrate the links between the various methods.
Biography:Michael Greenacre is Professor of Statistics at the
Universitat Pompeu Fabra in Barcelona. Apart from his normal teaching
duties, he has given courses on multivariate analysis to marine
biologists at the Polar Institute and the Norwegian College of Fishery
Science in Tromsø, Norway, also in Italy, Iceland and Spain. He has
participated as a statistician in various environmental research
projects and is a member of the ARCTOS network. His research interests
are in the analysis of large data sets in the social and environmental
sciences, having authored and co-edited six books and numerous journal
articles on correspondence analysis and data visualization. Recently,
the BBVA Foundation has published the Spanish translation of his latest
book (Correspondence Analysis in Practice, second edition, Chapman &
Hall, 2007), entitled La Práctica del Análisis de Correspondencias. He
is presently in Australia as a guest of the Australian Market and Social
Research Society.
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