fdata_rkhs {fpcb}

functional data in rkhs

Description

Representing functinal data using Reproducing Kernel Hilbert Spaces. Approximate each curve with a smooth function using a kernel function.

Usage

fdata_rkhs(curves, rk, gamma = 1e-05)

Arguments

curves

a data matrix with observations (curves) in rows and the discretizations points in columns.

rk

kernek function rk object.

gamma

regularization parameter. Defaoult value = 1e-5.

Details

With this function each function can be represented with a vector in R^d.

Value

data

input curves.

fdata

smoothed curves.

lambda

coefficients of the (stable) and d dimensional RKHS representation.

alpha

coefficients of the RKHS expansion.

gamma

regularization parameter.

Author(s)

N. Hernández and J. Cugliari

References

A. Muñoz, J. González, Representing functional data using support vector machines, Pattern Recognition Letters 31 (2010) 511–516. <doi:10.1016/j.patrec.2009.07.014>.

Examples

t = 1:50
curves = matrix(sin(t)+rnorm(length(t)),nrow=1)
f.data <- fdata_rkhs(curves, rk = rk(t,sigma = 0.01))
plot(t,curves, xlab='time', ylab='PM10 dataset', col='gray', lty=1, type='b')
lines(t,f.data$fdata, col='blue', lty=1)