fdata_rkhs function

functional data in rkhs

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

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.

Returns

• 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.

Details

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

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)

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.

Author(s)

N. Hernández and J. Cugliari