Robust principal component analysis for power transformed compositional data  

Authors / CoAuthors

Scealy, J. L. | de Caritat, P. | Grunsky, E. | Tsagris, M. T. | Welsh, A. H.

Abstract

Geochemical surveys collect sediment or rock samples, measure the concentration of chemical elements and report these typically either in weight percent or in parts per million. There are usually a large number of elements measured and the distributions are often skewed, containing many potential outliers. We present a new robust principal component analysis (PCA) method for geochemical survey data, which involves first transforming the compositional data onto various different manifolds using power transformations. A flexible set of moment assumptions are made which take the special geometry of each manifold into account. The Kent distribution moment structure arises as a special case when the chosen manifold is the hypersphere. We derive simple moment and robust estimators of the parameters which are also applicable in high dimensional settings. The resulting PCA based on these estimators is effectively done in the tangent space and is closely related to the power transformation method used in correspondence analysis. To illustrate, we analyse major oxide data from the National Geochemical Survey of Australia. When compared with the traditional approach in the literature based on the centred logratio transformation, the new PCA method is shown to be more successful at dimension reduction and gives more interpretable results.

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nonGeographicDataset

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76710

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• External Publication

• AU

Australian and New Zealand Standard Research Classification (ANZSRC)

• Earth Sciences

• Published_Internal

Publication Date

2014-01-01T00:00:00

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Australian Government Security ClassificationSystem    

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Creative Commons Attribution 4.0 International Licence    

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geoscientificInformation

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[-44.0, -10.0, 112.0, 154.0]

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