entropy.fd {bigdatadist}

Functional Entropy Measures

Description

This function allows you to compute the family of alpha-Entropy for functional data as stated in Martos et al (2018).

Usage

entropy.fd(fdframe, gamma = 1, kerfunc="rbf",
       kerpar = list(sigma = 1, bias=0,degree=2), 
       alpha=2,d=2,resol,k.neighbor) 

Arguments

fdframe

functional data frame fdframe object.

gamma

regularization parameter.

kerfunc

kernel function (rbf or poly) to be used.

kerpar

a list of kernel parameters where sigma is the scale with both kernels.

alpha

Entropy parameter.

d

Dimension truncation in the Reproducing Kernel Hilbert Space representation.

resol

number of level sets used to compute the functional entropy.

k.neighbor

number of points to estimate the support of the distribution.

Details

This function estimates the entropy of a stochastic process. To this aim, the raw functional data is projected onto a Reproducing Kernel Hilbert Space, and the entropy is estimated using the coefficient of these functions.

Value

local.entropy

local entropy relative to each curve in the sample.

entropy

estimated entropy of the the set of functions.

Author(s)

Hernandez and Martos

References

Martos, G. et al (2018). Entropy Measures for Stochastic Processes with Applications in Functional Anomaly Detection. Entropy 20(1), 33 (2018).

Examples

data(Ausmale); t <- Ausmale[[1]]
t <- as.numeric(( t - min(t) ) / length(t))
raw.data <- fdframe(t=t, Y=Ausmale[[2]])

entropy.fd(raw.data,gamma=0.0001,kerfunc="rbf",kerpar=c(10), 
                        alpha=2, k.neighbor=15)