Conformal Isomap(C-Isomap) is a variant of a celebrated method of Isomap. It aims at, rather than
preserving full isometry, maintaining infinitestimal angles - conformality - in that
it alters geodesic distance to reflect scale information.

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

## 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(dname="cswiss",n=100)
## 1. original Isomap
output1 <- do.isomap(X,ndim=2)
## 2. C-Isomap
output2 <- do.cisomap(X,ndim=2)
## 3. C-Isomap on a binarized graph
output3 <- do.cisomap(X,ndim=2,weight=FALSE)
## Visualize three different projections
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(output1$Y, main="Isomap")
plot(output2$Y, main="C-Isomap")
plot(output3$Y, main="Binarized C-Isomap")
par(opar)
# }
```