compositions (version 1.01-1)

gsi.merge2signary: Auxiliary functions to compute user-defined ilr and ipt transforms.

Description

Compute the basis of a clr-plane, to use with isometric log-ratio or planar transform of a (dataset of) compositions.

Usage

gsi.merge2signary( M )
          gsi.ilrBase2signary( V )
          gsi.optimalilrBase( x )
          gsi.buildilrBase( W=c(1,-1) )
          gsi.signary2ilrBase( W=c(1,-1) )
          gsi.OrderIlr( V )

Arguments

M

a merge structure (as explained in hclust)

x

a compositional data set

W

a signary matrix (as explained below) defining a partition

V

a matrix of change of basis from clr/cpt to ilr/ipt

Value

• These functions will not be usually called on themselves, but through their wrappers, mainly ilrBase. Functions gsi.merge2signary and gsi.ilrBase2signary return a signary matrix (as explained in "details"), gsi.optimalilrBase returns a merge structure (as epxlained in hclust), and gsi.buildilrBase (and its alias gsi.signary2ilrBase) returns an ilr matrix. These functions are thought to be called sequentially. Apart, gsi.OrderIlr reorders both parts and coordinates to ease dendrogram-like representations (see CoDaDendrogram).

Details

A signary matrix is a matrix with the same shape as an ilr matrix, but containing only +1, 0 or -1 values (thus, it is a kind of "extended binary"). If the value W[i,j]= +1, then part "i" is involved in coordinate "j" in the numerator; if W[i,j]=-1, it is involed in the denominator, and if W[i,j]=0 then part "i" does not take part in coordinate "j".

Functions gsi.merge2signary and gsi.buildilrBase are intended to compute ilrBase matrices associated to user-defined partition structures. Function gsi.ilrBase2signary offers the inverse functionality.

Function gsi.OrderIlr returns a list with two elements: "ilrBase" and "order". The first one contains the ilr basis with coordinates reordered in decreasing number of involved parts (so, all parts are involved in the first coordinate, and only two in the last). The second one gives a permutation of the parts so that involved parts in each coordinate are always together. Note that ilrBase does not have its parts permuted!

References

Egozcue J.J., V. Pawlowsky-Glahn, G. Mateu-Figueras and C. Barcel'o-Vidal (2003) Isometric logratio transformations for compositional data analysis. Mathematical Geology, 35(3) 279-300

See Also

ilrBase,ipt,ilr, http://ima.udg.es/Activitats/CoDaWork03

Examples

m <- matrix(data=c(-1,-2,
                  -3,-4,
                   1, 2),ncol=2,nrow=3,byrow=TRUE)
w <- gsi.merge2signary(m)
w
V=gsi.buildilrBase(w)
V
gsi.ilrBase2signary(V)
gsi.OrderIlr(V)