ade4 (version 1.7-19)

mld: Multi Level Decomposition of unidimensional data

Description

The function mld performs an additive decomposition of the input vector x onto sub-spaces associated to an orthonormal orthobasis. The sub-spaces are defined by levels of the input factor level. The function haar2level builds the factor level such that the multi level decomposition corresponds exactly to a multiresolution analysis performed with the haar basis.

Usage

mld(x, orthobas, level, na.action = c("fail", "mean"),
 plot = TRUE, dfxy = NULL, phylog = NULL, ...)
haar2level(x)

Value

A data frame with the components resulting from the decomposition.

Arguments

x

is a vector or a time serie containing the data to be decomposed. This must be a dyadic length vector (power of 2) for the function haar2level.

orthobas

is a data frame containing the vectors of the orthonormal basis.

level

is a factor which levels define the sub-spaces on which the function mld performs the additive decomposition.

na.action

if 'fail' stops the execution of the current expression when x contains any missing value. If 'mean' replaces any missing values by mean(x).

plot

if TRUE plot x and the components resulting from the decomposition.

dfxy

is a data frame with two coordinates.

phylog

is an object of class phylog.

...

further arguments passed to or from other methods.

Author

Sébastien Ollier

References

Mallat, S. G. (1989) A theory for multiresolution signal decomposition: the wavelet representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11, 7, 674--693.

Percival, D. B. and Walden, A. T. (2000) Wavelet Methods for Time Series Analysis, Cambridge University Press.

See Also

gridrowcol, orthobasis, orthogram, mra for multiresolution analysis with various families of wavelets

Examples

if (FALSE) {
# decomposition of a time serie
data(co2)
x <- log(co2)
orthobas <- orthobasis.line(length(x))
level<-rep("D", 467)
level[1:3]<-rep("A", 3)
level[c(77,78,79,81)]<-rep("B", 4)
level[156]<-"C"
level<-as.factor(level)
res <- mld(x, orthobas, level)
sum(scale(x, scale = FALSE) - apply(res, 1, sum))
}
# decomposition of a biological trait on a phylogeny
data(palm)
vfruit<-palm$traits$vfruit
vfruit<-scalewt(vfruit)   
palm.phy<-newick2phylog(palm$tre)
level <- rep("F", 65)
level[c(4, 21, 3, 6, 13)] <- LETTERS[1:5]
level <- as.factor(level)
res <- mld(as.vector(vfruit), palm.phy$Bscores, level,
 phylog = palm.phy, clabel.nod = 0.7, f.phylog=0.8,
  csize = 2, clabel.row = 0.7, clabel.col = 0.7)