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.

Kisung You

## 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)
# }