Isometric log transform
Compute the isometric log transform of a vector (dataset) of amounts and its inverse.
ilt( x ,...)
iltInv( z ,... )x |
a vector or data matrix of amounts |
z |
the ilt-transform of a vector or data matrix of ilt-transforms of amounts |
... |
generic arguments, not used. |
The ilt-transform maps D amounts (considered in log geometry)
isometrically to a D dimensional euclidean vector. The ilt is
part of the aplus framework.
The data can then be analysed in this transformation by all classical
multivariate analysis tools. The interpretation of the results is easy
since the relation to the original
variables is preserved.
The isometric log transform is given by
ilt(x)_i := \ln x_i
ilt gives the isometric log transform, i.e. simply the log of
the argument, whereas
iltInv gives amounts with the given ilt, i.e. simply the exp
of the argument.
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.
(tmp <- ilt(c(1,2,3))) iltInv(tmp) iltInv(tmp) - c(1,2,3) # 0 data(Hydrochem) cdata <- Hydrochem[,6:19] pairs(ilt(cdata))
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