nonlinear_MVE: Minimum Volume Embedding

In kisungyou/Rdimtools: Dimension Reduction and Estimation Methods

Minimum Volume Embedding

Description

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 ∑ λ_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.

Usage

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.

Author(s)

Kisung You

References

\insertRef

shaw_minimum_2007Rdimtools

See Also

do.mvu

Examples

## Not run: 
## 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)

## End(Not run)

kisungyou/Rdimtools documentation built on Jan. 2, 2023, 9:55 a.m.