metric.hausdorff
Compute the Hausdorff distances between two curves.
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).
- Keywords
- cluster
Usage
metric.hausdorff(fdata1, fdata2 = fdata1)
Arguments
- fdata1
Curves 1 of
fdata
class. The dimension offdata1
object is (n1
xm
), wheren1
is the number of points observed int
coordinates with lenghtm
.- fdata2
Curves 2 of
fdata
class. The dimension offdata2
object is (n2
xm
), wheren2
is the number of points observed int
coordinates with lenghtm
.
Details
Let \(G(X)=\left\{ (t,X(t))\in R^2 \right\}\) and \(G(Y)=\left\{(t,Y(t))\in R^2\right\}\) be two graphs of the considered curves \(X\) and \(Y\) respectively, the Hausdorff distance \(d_H(X, Y)\) is defined as,
$$ d_H(X,Y)=max\left\{ sup_{x\in G(X)} inf_{y\in G(Y)} d_2(x,y),
sup_{y\in G(Y)} inf_{x\in G(X)}d_2(x,y)\right\},$$
where \(d_2(x,y)\) is the euclidean distance, see metric.lp.
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)))
# }
# NOT RUN {
# }