Minimum Volume Embedding

Minimum Volume Embedding (MVE) is a nonlinear dimension reduction algorithm that exploits semidefinite programming (SDP), like MVU/SDE. Whereas MVU aims at stretching through all direction by maximizing \(\sum \lambda_i\), MVE only opts for unrolling the top eigenspectrum and chooses to shrink left-over spectral dimension. For ease of use, unlike kernel PCA, we only made use of Gaussian kernel for MVE.

do.mve(
  X,
  ndim = 2,
  knn = ceiling(nrow(X)/10),
  kwidth = 1,
  preprocess = c("null", "center", "scale", "cscale", "whiten", "decorrelate"),
  tol = 1e-04,
  maxiter = 10
)

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.

knn

size of \(k\)-nn neighborhood.

kwidth

bandwidth for Gaussian kernel.

preprocess

an additional option for preprocessing the data. Default is "null". See also aux.preprocess for more details.

tol

stopping criterion for incremental change.

maxiter

maximum number of iterations allowed.

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

Shaw B, Jebara T (2007). “Minimum Volume Embedding.” In Meila M, Shen X (eds.), Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics March 21-24, 2007, San Juan, Puerto Rico, 460--467.

See also

do.mvu

Author

Kisung You

Examples

if (FALSE) {
## use a small subset of iris data
set.seed(100)
id  = sample(1:150, 50)
X   = as.matrix(iris[id,1:4])
lab = as.factor(iris[id,5])

## try different connectivity levels
output1 <- do.mve(X, knn=5)
output2 <- do.mve(X, knn=10)
output3 <- do.mve(X, knn=20)

## Visualize two comparisons
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(output1$Y, main="knn:k=5",  pch=19, col=lab)
plot(output2$Y, main="knn:k=10", pch=19, col=lab)
plot(output3$Y, main="knn:k=20", pch=19, col=lab)
par(opar)
}