Landmark Isomap is a variant of Isomap in that
it first finds a low-dimensional embedding using a small portion of given dataset
and graft the others in a manner to preserve as much pairwise distance from
all the other data points to landmark points as possible.

```
do.lisomap(
X,
ndim = 2,
ltype = c("random", "MaxMin"),
npoints = max(nrow(X)/5, ndim + 1),
preprocess = c("center", "scale", "cscale", "decorrelate", "whiten"),
type = c("proportion", 0.1),
symmetric = c("union", "intersect", "asymmetric"),
weight = TRUE
)
```

## 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.

- ltype
on how to select landmark points, either `"random"`

or `"MaxMin"`

.

- npoints
the number of landmark points to be drawn.

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

for more details.

- 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 Landmark Isomap on weighted graph, or `FALSE`

otherwise.

## 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{
## use iris data
data(iris)
X <- as.matrix(iris[,1:4])
lab <- as.factor(iris[,5])
## use different number of data points as landmarks
output1 <- do.lisomap(X, npoints=10, type=c("proportion",0.25))
output2 <- do.lisomap(X, npoints=25, type=c("proportion",0.25))
output3 <- do.lisomap(X, npoints=50, type=c("proportion",0.25))
## visualize three different projections
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(output1$Y, pch=19, col=lab, main="10 landmarks")
plot(output2$Y, pch=19, col=lab, main="25 landmarks")
plot(output3$Y, pch=19, col=lab, main="50 landmarks")
par(opar)
# }
```