Distinguishing Variance Embedding (DVE) is an unsupervised nonlinear manifold learning method.
It can be considered as a balancing method between Maximum Variance Unfolding and Laplacian
Eigenmaps. The algorithm unfolds the data by maximizing the global variance subject to the
locality-preserving constraint. Instead of defining certain kernel, it applies local scaling scheme
in that it automatically computes adaptive neighborhood-based kernel bandwidth.

```
do.dve(
X,
ndim = 2,
type = c("proportion", 0.1),
preprocess = c("null", "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.

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

Wang Q, Li J (2009).
“Combining Local and Global Information for Nonlinear Dimensionality Reduction.”
*Neurocomputing*, **72**(10-12), 2235--2241.

Qinggang W, Jianwei L, Xuchu W (2010).
“Distinguishing Variance Embedding.”
*Image and Vision Computing*, **28**(6), 872--880.

## Examples

```
# \donttest{
## generate swiss-roll dataset of size 100
set.seed(100)
X <- aux.gensamples(dname="crown", n=100)
## try different nbd size
out1 <- do.dve(X, type=c("proportion",0.5))
out2 <- do.dve(X, type=c("proportion",0.7))
out3 <- do.dve(X, type=c("proportion",0.9))
## visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(out1$Y, main="50% connected")
plot(out2$Y, main="70% connected")
plot(out3$Y, main="90% connected")
par(opar)
# }
```