fda.usc: metric.lp – R documentation

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metric.lp

Approximates Lp-metric distances for functional data.

Description

Measures the proximity between the functional data and curves approximating Lp-metric. If w = 1 approximates the Lp-metric by Simpson's rule. By default it uses lp = 2 and weights w = 1.

Usage

metric.lp(fdata1, fdata2 = NULL, lp = 2, w = 1, dscale = 1, ...)

Arguments

`fdata1`	Functional data 1 or curve 1. If `fdata` class, the dimension of `fdata1$data` object is (`n1` x `m`), where `n1` is the number of curves and `m` are the points observed in each curve.
`fdata2`	Functional data 2 or curve 2. If `fdata` class, the dimension of `fdata2$data` object is (`n2` x `m`), where `n2` is the number of curves and `m` are the points observed in each curve.
`lp`	Lp norm, by default it uses `lp = 2`
`w`	Vector of weights with length `m`, If `w = 1` approximates the metric Lp by Simpson's rule. By default it uses `w = 1`
`dscale`	If scale is a numeric, the distance matrix is divided by the scale value. If scale is a function (as the mean for example) the distance matrix is divided by the corresponding value from the output of the function.
`...`	Further arguments passed to or from other methods.

Details

By default it uses the L2-norm with lp = 2.

f(x)= fdata1(x)-fdata2(x)

The observed points on each curve are equally spaced (by default) or not.

The L∞-norm is computed with lp = 0.

d(fdata1(x),fdata2(x))_{∞}=sup ≤ft|fdata1(x)-fdata2(x)\right|

Author(s)

Manuel Febrero-Bande, Manuel Oviedo de la Fuente manuel.oviedo@usc.es

References

Febrero-Bande, M., Oviedo de la Fuente, M. (2012). Statistical Computing in Functional Data Analysis: The R Package fda.usc. Journal of Statistical Software, 51(4), 1-28. http://www.jstatsoft.org/v51/i04/

Examples

## Not run: 
#	INFERENCE PHONDAT
data(phoneme)
mlearn<-phoneme$learn[1:100]
mtest<-phoneme$test[1:100]
glearn<-phoneme$classlearn[1:100]
gtest<-phoneme$classtest[1:100]
# Matrix of distances of curves of DATA1
mdist1<-metric.lp(mlearn)

# Matrix of distances between curves of DATA1 and curves of DATA2
mdist2<-metric.lp(mlearn,mtest,lp=2)
# mdist with L1 norm and weigth=v
v=dnorm(seq(-3,3,len=dim(mlearn)[2]))
mdist3<-metric.lp(mlearn,mtest,lp=1,w=v)
plot(1:100,mdist2[1,],type="l",ylim=c(1,max(mdist3[1,])))
lines(mdist3[1,],type="l",col="2")

# mdist with mlearn with different discretization points.
# mlearn2=mlearn
# mlearn2[["argvals"]]=seq(0,1,len=150)
# mdist5<-metric.lp(mlearn,mlearn2)
# mdist6<-metric.lp(mlearn2,mlearn) 
# sum(mdist5-mdist6)
# sum(mdist1-mdist6)

x<-seq(0,2*pi,length=1001)
fx<-fdata(sin(x)/sqrt(pi),x)
fx0<-fdata(rep(0,length(x)),x)
metric.lp(fx,fx0)
# The same
integrate(function(x){(abs(sin(x)/sqrt(pi))^2)},0,2*pi)

## End(Not run)

fda.usc

Functional Data Analysis and Utilities for Statistical Computing

v2.0.2

GPL-2

Authors

Manuel Febrero Bande [aut], Manuel Oviedo de la Fuente [aut, cre], Pedro Galeano [ctb], Alicia Nieto [ctb], Eduardo Garcia-Portugues [ctb]

Initial release

2020-02-17