The canonical basis in the clr plane used for ilr and ipt transforms.
Compute the basis of a clr-plane, to use with isometric log-ratio or planar transform of a (dataset of) compositions.
gsi.PrinBal( x, method="PBhclust" )
a data set (required)
method to build the principal balances; currently, one of "PBhclust", "PBmaxvar" or "PBangprox"
Method "PBhclust" generates a Ward cluster analysis of the parts (not of the observations!) using as distance between parts the variation matrix.
Method "PBmaxvar" splits all parts in two groups after a PCA (those with positive weight against those with negative weight in the first PC), and then checks for each element whether moving it increases the variance of the resulting balance. The largest variance balance is chosen. That variance is removed, and each of the groups of parts is analysed recursively.
Method "angprox" calculates all possible balances (exhaustive combinations of "ncol(x)" elements split in three groups: +1, 0 and -1), and computes their angles with the first PC. The nearest balance is chosen. Its variance is substracted, and the algorithm is repeated recursively ensuring orthogonality of the next splittings with respect to the balances already chosen. This method creates a temporary file ".APtable" that can be removed after execution (or copypasted in your logfiles).
Note that more methods can appear in the future, and that, except "PBhclust", all methods can be VERY slow. Extensive reprogramming of these routines can be expected in the future.
All methods give a matrix containing by columns the basis elements for the canonical basis of the clr-plane used for the ilr and ipt transform. Principal Balances are balance bases approximating Principal Component in certain ways, depending on the specific method chosen.
J.J. Egozcue (programming "PBmaxvar") and R. Tolosana-Delgado (programming other methods and wrapper)
Pawlowsky-Glahn, V., J.J. Egozcue and R. Tolosana-Delgado (2011) Principal Balances. In: Egozcue, J.J., R. Tolosana-Delgado and M.I. Ortego (eds) Proceedings of CoDaWork'2011, the 4th International Workshop on Compositional Data Analysis. CIMNE, Barcelona (E)
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