Example programs and commands
		 Multidimensional scaling with Isomap

# All lines preceded by the "#" character are comments or output.
# All other left-justified lines are my input

###################### Isomap in R ############
#
# Isomap builds a graph from the data, connecting only nearby points
# with edges.

install.packages("vegan")    # This contains "isomap()"
library(vegan)

### Build the isomap graphs for 3 iris species

data(iris);  # Recall: 3 species, 50 plants each, 4-variate data

# Isomap graphs, k=3 nearest neighbors by Euclidean distance

y<-iris[iris$Species=="setosa",1:4]
idist <- dist(y); imap<-isomap(idist,k=3); plot(imap)

y<-iris[iris$Species=="versicolor",1:4]
idist <- dist(y); imap<-isomap(idist,k=3); plot(imap)

y<-iris[iris$Species=="virginica",1:4]
idist <- dist(y); imap<-isomap(idist,k=3); plot(imap)


%%%%%%%%%%%%%%%%%%%%%  cmdscale() in Octave

pkg load statistics
D=zeros(8,8);
for i=1:8
 for j=1:8
   D(i,j)=abs(i-j);
 end
end

Y=cmdscale(D)