Compute the basis of a clr-plane, to use with isometric log-ratio or planar transform of a (dataset of) compositions.
gsi.merge2signary( M )
gsi.ilrBase2signary( V )
gsi.optimalilrBase( x )
gsi.buildilrBase( W=c(1,-1) )
gsi.signary2ilrBase( W=c(1,-1) )
gsi.OrderIlr( V )
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
).
a merge structure (as explained in hclust
)
a compositional data set
a signary matrix (as explained below) defining a partition
a matrix of change of basis from clr/cpt to ilr/ipt
Raimon Tolosana-Delgado, K.Gerald v.d. Boogaart http://www.stat.boogaart.de
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!
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
ilrBase
,ipt
,ilr
,
https://ima.udg.edu/Activitats/CoDaWork03/
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)
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