Multi Level Decomposition of unidimensional data

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)

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.

Value

A data frame with the components resulting from the decomposition.

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.

Author

Sébastien Ollier sebastien.ollier@u-psud.fr

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)