nonlinear_BMDS: Bayesian Multidimensional Scaling

In Rdimtools: Dimension Reduction and Estimation Methods

Bayesian Multidimensional Scaling

Description

A Bayesian formulation of classical Multidimensional Scaling is presented. Even though this method is based on MCMC sampling, we only return maximum a posterior (MAP) estimate that maximizes the posterior distribution. Due to its nature without any special tuning, increasing mc.iter requires much computation. A note on the method is that this algorithm does not return an explicit form of projection matrix so it's classified in our package as a nonlinear method. Also, automatic dimension selection is not supported for simplicity as well as consistency with other methods in the package.

Usage

do.bmds(
  X,
  ndim = 2,
  par.a = 5,
  par.alpha = 0.5,
  par.step = 1,
  mc.iter = 50,
  print.progress = FALSE
)

Arguments

X	an (n\times p) matrix whose rows are observations and columns represent independent variables.
ndim	an integer-valued target dimension.
par.a	hyperparameter for conjugate prior on variance term, i.e., σ^2 \sim IG(a,b). Note that b is chosen appropriately as in paper.
par.alpha	hyperparameter for conjugate prior on diagonal term, i.e., λ_j \sim IG(α, β_j). Note that β_j is chosen appropriately as in paper.
par.step	stepsize for random-walk, which is standard deviation of Gaussian proposal.
mc.iter	the number of MCMC iterations.
print.progress	a logical; TRUE to show iterations, FALSE otherwise (default: FALSE).

Value

a named Rdimtools S3 object containing

Y

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

algorithm

name of the algorithm.

Author(s)

Kisung You

References

\insertRef

oh_bayesian_2001Rdimtools

Examples

## load 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])

## compare with other methods
outBMD <- do.bmds(X, ndim=2)
outPCA <- do.pca(X, ndim=2)
outLDA <- do.lda(X, label, ndim=2)

## visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(outBMD$Y, pch=19, col=label, main="Bayesian MDS")
plot(outPCA$Y, pch=19, col=label, main="PCA")
plot(outLDA$Y, pch=19, col=label, main="LDA")
par(opar)

Rdimtools documentation built on Dec. 28, 2022, 1:44 a.m.