Karhunen_Loeve: Karhunen Loeve expansion

In elamrireda/FunctQuant: Data-Driven Functional Quantization

Description

Dimension reduction : Karhunen Loeve expansion

Usage

Karhunen_Loeve(data,mKL,scale=TRUE)

Arguments

data	matrix that we want to quantize.
mKL	truncation argument for the dimension reduction.
scale	scale or not the input data.

Value

Coeff	the coefficient in the reduced space.
ExplainedVar	the explained variance.
center	the mean curve.
eigenfunction	the eigenfunctions.

Examples

##### function to generate realizations of BM
BM <- function(N=1000,M=1,x0=0,t0=0,T=1,Dt=NULL)
{
  Dt <- (T - t0)/N
  t <- seq(t0, T, by=Dt)
  res <- data.frame(sapply(1:M,function(i) c(0,cumsum(rnorm(N,mean  =0,sd=sqrt(Dt))))))
  names(res) <- paste("X",1:M,sep="")
  X <- ts(res, start = t0, deltat = Dt)
  return(X)
}
data <- t(BM(N = 200 - 1, M = 200))
mKL <- 2
DimReduction <- Karhunen_Loeve(data,mKL,scale=TRUE)

elamrireda/FunctQuant documentation built on Jan. 1, 2021, 2:50 p.m.