fdata_rkhs: functional data in rkhs

In fpcb: Predictive Confidence Bands for Functional Time Series Forecasting

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)

fpcb documentation built on June 7, 2021, 9:08 a.m.