`do.isomap`

is an efficient implementation of a well-known *Isomap* method
by Tenenbaum et al (2000). Its novelty comes from applying classical multidimensional
scaling on nonlinear manifold, which is approximated as a graph.

```
do.isomap(
X,
ndim = 2,
type = c("proportion", 0.1),
symmetric = c("union", "intersect", "asymmetric"),
weight = FALSE,
preprocess = c("center", "scale", "cscale", "decorrelate", "whiten")
)
```

## Arguments

- X
an \((n\times p)\) matrix or data frame whose rows are observations
and columns represent independent variables.

- ndim
an integer-valued target dimension.

- type
a vector of neighborhood graph construction. Following types are supported;
`c("knn",k)`

, `c("enn",radius)`

, and `c("proportion",ratio)`

.
Default is `c("proportion",0.1)`

, connecting about 1/10 of nearest data points
among all data points. See also `aux.graphnbd`

for more details.

- symmetric
one of `"intersect"`

, `"union"`

or `"asymmetric"`

is supported. Default is `"union"`

. See also `aux.graphnbd`

for more details.

- weight
`TRUE`

to perform Isomap on weighted graph, or `FALSE`

otherwise.

- preprocess
an additional option for preprocessing the data.
Default is "center". See also `aux.preprocess`

for more details.

## Value

a named list containing

- Y
an \((n\times ndim)\) matrix whose rows are embedded observations.

- trfinfo
a list containing information for out-of-sample prediction.

## References

Silva VD, Tenenbaum JB (2003).
“Global Versus Local Methods in Nonlinear Dimensionality Reduction.”
In Becker S, Thrun S, Obermayer K (eds.), *Advances in Neural Information Processing Systems 15*, 721--728.
MIT Press.

## Examples

```
# \donttest{
## generate data
set.seed(100)
X <- aux.gensamples(n=123)
## 1. connecting 10% of data for graph construction.
output1 <- do.isomap(X,ndim=2,type=c("proportion",0.10),weight=FALSE)
## 2. constructing 25%-connected graph
output2 <- do.isomap(X,ndim=2,type=c("proportion",0.25),weight=FALSE)
## 3. constructing 25%-connected with binarization
output3 <- do.isomap(X,ndim=2,type=c("proportion",0.50),weight=FALSE)
## Visualize three different projections
opar = par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(output1$Y, main="10%")
plot(output2$Y, main="25%")
plot(output3$Y, main="25%+Binary")
par(opar)
# }
```