Australian Male Mortality Rates

Description

The data consist of set of measurements across years of male mortality rates in Australia from package fds.

Usage

Ausmale

Format

A list with years in the first component and a 101 times 103 matrix, years in rows and cohorts in columns, in the second component.

Source

fds

Entropy Computation

Description

This function allows you to compute the family of alpha entropy as stated in Martos et al (2018).

Usage

entropy(X,alpha=2,k.neighbor,scale=FALSE) 

Arguments

Details

The function computes the alpha entropy and the local alpha entropy (see reference for further details) of a data set using a non parametric density estimator.

Value

References

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

Examples

require(MASS);
data = mvrnorm(100,c(0,0),diag(2));
entropy(data, alpha = 2, k.neighbor = 10, scale = FALSE)

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

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

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)

Functional Data Frame

Description

This function is used to create multivariate functional data frame objects to be used in combination with the functions in the package bigdatadist.

Usage

fdframe(t, Y)

Arguments

Examples

t = 1:10; Y = cbind(sin(t),cos(t))
fdata = fdframe(t,Y)
plot(fdata, xlab='Time', ylab='')

Generalized Mahalanobis Depth and Distance

Description

This function allows you to compute the Generalized Kernel Mahalanobis depth measure as stated in Hernandez et al (2018, submitted) and the Generalized Mahalanobis distance in Martos et al (2014).

Usage

gmdepth(A,b,resol,k.neighbor) 

Arguments

Value

Author(s)

Hernandez and Martos

References

Hernandez N. et al (2018). Generalized Mahalanobis depth functions (submitted). Martos, G. et al (2014). Generalizing the Mahalanobis distance via density kernels. Inteligent Data Anal.

Examples

require(MASS)
set.seed(1)
A=mvrnorm(450,c(0,0),Sigma=diag(2))
b=mvrnorm(50,c(10,10),Sigma=diag(c(0.1,0.1)))
C=rbind(A,b)
plot(C, pch=20, col=c(rep('black',450),rep('red',50)),
                      xlab='x1',ylab='x2')

gmd.fit = gmdepth(A=C)
depth    = gmd.fit$depth
distance = gmd.fit$distance
plot(depth,distance, pch=20, 
           col=c(rep('black',450),rep('red',50)))
gmdepth(A=A,b=mvrnorm(1,c(0,0),Sigma=diag(2))) 

Generalized Mahalanobis Kernel Depth and Distance for Functional Data

Description

This function allows you to compute the Generalized Kernel Mahalanobis depth measure as stated in Hernandez et al (2018, submitted) and the Generalized Mahalanobis distance in Martos et al (2014), for functional data represented in a Reproducing Kernel Hilbert Space.

Usage

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

Arguments

Value

Author(s)

Hernandez and Martos

References

Hernandez N. et al (2018, submitted). Generalized Mahalanobis depth functions. Martos, G. et al (2014). Generalizing the Mahalanobis distance via density kernels. Inteligent Data Anal.

Examples

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

gmd.fit.fd = gmdepth.fd(raw.data,gamma=0.001,
            kerfunc="rbf",kerpar=list(sigma = 10))

gmd.fit.fd$distance
gmd.fit.fd$depth

rbPal <- colorRampPalette(c('red','black'))
color = rbPal(5)[as.numeric(cut(gmd.fit.fd$depth,breaks = 5))]
plot(rkhs(raw.data,gamma=0.0001,kerfunc="rbf",kerpar=list(sigma = 10)),
 col = color, xlab='time',ylab='')

Kernel Mahalanobis Depth for Functional Data

Description

This function allows you to compute the Generalized Kernel Mahalanobis depth measure for a sample of functional data as stated in Hernandez et al (2018, submitted).

Usage

kmdepth.fd(fdframe, gamma = 1, kerfunc = "rbf" ,
                        kerpar = list(sigma = 1, bias = 0, degree = 2) ,
                        d = 2 , robust=TRUE , h=0.1 , nsamp=250)  

Arguments

Value

Author(s)

Hernandez and Martos

References

Hernandez N. et al (2018, submitted). Generalized Mahalanobis depth functions.

Examples

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

kmd.fit.fd = kmdepth.fd(raw.data, gamma = 0.0001, kerfunc = "rbf" ,
                        kerpar = list(sigma = 10) , d = 2 , robust=TRUE)  

kmd.fit.fd$depth

rbPal <- colorRampPalette(c('red','black'))
color = rbPal(5)[as.numeric(cut(kmd.fit.fd$depth,breaks = 5))]
plot(rkhs(raw.data,gamma=0.0001,kerfunc="rbf",kerpar=list(sigma = 10)),
 col = color, xlab='time',ylab='')

Level Set Distances

Description

This function allows you to compute the alpha level set distances as proposed in Martos et al. Nomparametric distances for probability measures with applications, 2018 (submitted).

Usage

levelsetdist(A,B,n.level=10,k.neighbor=10) 

Arguments

Details

The function computes the alpha level set distance between two (samples from) different probability measures. Details about the distance and the criterion to fix its hyperparameter can be found in Martos et al (2018, submitted).

Value

References

Martos, G. et al (2018): Nomparametric distances for probability measures with applications in classification. J. of Calssification, 2018 (submitted).

Examples

require(MASS);
set.seed(1)
A = mvrnorm(100,c(0,0),diag(2));  B = mvrnorm(150,c(1,1),diag(2)); 
levelsetdist(A, B)

Merval Index

Description

The data consist of an low and high values of the Merval Index stock market from Argentina; the data were gathered from Yahoo Finance.

Usage

merval

Format

A dataframe with 5269 observations with daily minimum, maximum, open and close index values.

Source

Yahoo Finance

RKHS Representation

Description

This function allows you to fit discrete functional data (fdframe) as functions in RKHS solving a regularization problem as stated in Munoz (2010).

Usage

rkhs(fdframe, gamma=1, kerfunc='rbf', 
            kerpar=list(sigma=1, bias=0, degree=2))

Arguments

Value

Author(s)

Hernandez and Martos

References

Munoz A. et al (2010). Representing functional data using support vector machines. Pattern recognition letters, 31(6).

Examples

data(merval); t <- as.Date(merval[1:100,1])
t <- as.numeric(( t - min(t) ) / 154)
raw.data <-fdframe(t = t, Y = merval[1:100,2:5])
plot(raw.data, xlab='time', ylab='Merval raw data')

f.data <- rkhs(raw.data, gamma = 0.001, kerpar = list(sigma = 8))

print(f.data)

plot(f.data, xlab='time', ylab='Merval data')