fda.usc: metric.hausdorff – R documentation

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metric.hausdorff

Compute the Hausdorff distances between two curves.

Description

Hausdorff distance is the greatest of all the distances from a point in one curve to the closest point in the other curve (been closest the euclidean distance).

Usage

metric.hausdorff(fdata1, fdata2 = fdata1)

Arguments

`fdata1`	Curves 1 of `fdata` class. The dimension of `fdata1` object is (`n1` x `m`), where `n1` is the number of points observed in `t` coordinates with lenght `m`.
`fdata2`	Curves 2 of `fdata` class. The dimension of `fdata2` object is (`n2` x `m`), where `n2` is the number of points observed in `t` coordinates with lenght `m`.

Details

Let G(X)={(t,X(t)) \in R^2} and G(Y)={(s,Y(s)) \in R^2} be two graphs of the considered curves X and Y respectively, the Hausdorff distance d_H(X, Y) is defined as,

d_H(X,Y)=max{sup_{x\in G(X)} inf_{y\in G(Y)}d_2(x,y),sup_{y\in G(Y)} inf_{x\in G(X)}d_2(x,y)},

where d_2(x,y) is the euclidean distance, see metric.lp.

Author(s)

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

Examples

## Not run:    
data(poblenou)
nox<-poblenou$nox[1:6]
# Hausdorff vs maximum distance
out1<-metric.hausdorff(nox)       
out2<-metric.lp(nox,lp=0) 
out1
out2
par(mfrow=c(1,3))
plot(nox)
plot(hclust(as.dist(out1)))
plot(hclust(as.dist(out2)))

## 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