Distinguishing Variance Embedding

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.

Author

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)
# }