nonlinear_REE: Robust Euclidean Embedding

In kisungyou/Rdimtools: Dimension Reduction and Estimation Methods

Robust Euclidean Embedding

Description

Robust Euclidean Embedding (REE) is an embedding procedure exploiting robustness of \ell_1 cost function. In our implementation, we adopted a generalized version with weight matrix to be applied as well. Its original paper introduced a subgradient algorithm to overcome memory-intensive nature of original semidefinite programming formulation.

Usage

do.ree(
  X,
  ndim = 2,
  W = NA,
  preprocess = c("null", "center", "scale", "cscale", "whiten", "decorrelate"),
  initc = 1,
  dmethod = c("euclidean", "maximum", "manhattan", "canberra", "binary", "minkowski"),
  maxiter = 100,
  abstol = 0.001
)

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.
W	an (n\times n) weight matrix. Default is uniform weight of 1s.
preprocess	an additional option for preprocessing the data. Default is "null". See also aux.preprocess for more details.
initc	initial c value for subgradient iterating stepsize, c/√{i}.
dmethod	a type of distance measure. See dist for more details.
maxiter	maximum number of iterations for subgradient descent method.
abstol	stopping criterion for subgradient descent method.

Value

a named list containing

Y

an (n\times ndim) matrix whose rows are embedded observations.

niter

the number of iterations taken til convergence.

trfinfo

a list containing information for out-of-sample prediction.

Author(s)

Kisung You

References

\insertRef

cayton_robust_2006Rdimtools

Examples

## use iris data
data(iris)
set.seed(100)
subid = sample(1:150,50)
X     = as.matrix(iris[subid,1:4])
label = as.factor(iris[subid,5])

## try different distance method
output1 <- do.ree(X, maxiter=50, dmethod="euclidean")
output2 <- do.ree(X, maxiter=50, dmethod="maximum")
output3 <- do.ree(X, maxiter=50, dmethod="canberra")

## visualize three different projections
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(output1$Y, col=label, pch=19, main="dmethod-euclidean")
plot(output2$Y, col=label, pch=19, main="dmethod-maximum")
plot(output3$Y, col=label, pch=19, main="dmethod-canberra")
par(opar)

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