# metric.hausdorff

0th

Percentile

##### 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 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 $$G(X)=\left\{ (t,X(t))\in R^2 \right\}$$ 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.

##### Aliases
• metric.hausdorff
##### 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 {
# }

Documentation reproduced from package fda.usc, version 2.0.1, License: GPL-2

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