entropy.fd: Functional Entropy Measures

In bigdatadist: Distances for Machine Learning and Statistics in the Context of Big Data

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)

bigdatadist documentation built on May 2, 2019, 11:06 a.m.