metric.hausdorff: Compute the Hausdorff distances between two curves.

In fda.usc: Functional Data Analysis and Utilities for Statistical Computing

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 [e-mail]

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 documentation built on Oct. 17, 2022, 9:06 a.m.