`do.spmds`

transfers the classical multidimensional scaling problem into
the data spectral domain using Laplace-Beltrami operator. Its flexibility
to use subsamples and spectral interpolation of non-reference data enables relatively
efficient computation for large-scale data.

```
do.spmds(
X,
ndim = 2,
neigs = max(2, nrow(X)/10),
ratio = 0.1,
preprocess = c("null", "center", "scale", "cscale", "decorrelate", "whiten"),
type = c("proportion", 0.1),
symmetric = c("union", "intersect", "asymmetric")
)
```

## 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.

- neigs
number of eigenvectors to be used as *spectral dimension*.

- ratio
percentage of subsamples as reference points.

- preprocess
an additional option for preprocessing the data.
Default is `"null"`

. 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.

## 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

Aflalo Y, Kimmel R (2013).
“Spectral Multidimensional Scaling.”
*Proceedings of the National Academy of Sciences*, **110**(45), 18052--18057.

## Examples

```
if (FALSE) {
## Replicate the numerical example from the paper
# Data Preparation
set.seed(100)
dim.true = 3 # true dimension
dim.embed = 100 # embedding space (high-d)
npoints = 1000 # number of samples to be generated
v = matrix(runif(dim.embed*dim.true),ncol=dim.embed)
coeff = matrix(runif(dim.true*npoints), ncol=dim.true)
X = coeff%*%v
# see the effect of neighborhood size
out1 = do.spmds(X, neigs=100, type=c("proportion",0.10))
out2 = do.spmds(X, neigs=100, type=c("proportion",0.25))
out3 = do.spmds(X, neigs=100, type=c("proportion",0.50))
# visualize the results
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(out1$Y, main="10% neighborhood")
plot(out2$Y, main="25% neighborhood")
plot(out3$Y, main="50% neighborhood")
par(opar)
}
```