Compute the centered planar transform of a (dataset of) compositions and its inverse.
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a composition or a data.matrix of compositions, not necessarily closed
the cpt-transform of a composition or a data matrix of cpt-transforms of compositions. It is checked that the z sum up to 0.
generic arguments. not used.
The cpt-transform maps a composition in the D-part real-simplex
isometrically to a D-1 dimensional euclidian vector space, identified with a plane parallel
to the simplex but passing through the origin. However the
transformation is not injective and does not even reach the whole
plane. Thus resulting covariance matrices are always singular.
The data can then
be analysed in this transformed space by all classical multivariate
analysis tools not relying on a full rank of the covariance matrix. See
apt for alternatives. The
interpretation of the results is relatively easy since the relation of each
transformed component to the original parts is preserved.
The centered planar transform is given by
cpt(x)_i := clo(x)_i - 1/D
cpt gives the centered planar transform,
cptInv gives closed compositions with the given cpt-transforms.
K.Gerald v.d. Boogaart http://www.stat.boogaart.de
van den Boogaart, K.G. and R. Tolosana-Delgado (2008) "compositions": a unified R package to analyze Compositional Data, Computers & Geosciences, 34 (4), pages 320-338, doi:10.1016/j.cageo.2006.11.017.
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