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) { # \dontrun{
# 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)