bmds: Bayesian Multidimensional Scaling

In maotai: Tools for Matrix Algebra, Optimization and Inference

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.

Usage

bmds(
  data,
  ndim = 2,
  par.a = 5,
  par.alpha = 0.5,
  par.step = 1,
  mc.iter = 8128,
  verbose = TRUE
)

Arguments

data	an (n\times p) matrix whose rows are observations.
ndim	an integer-valued target dimension.
par.a	hyperparameter for conjugate prior on variance term, i.e., \sigma^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., \lambda_j \sim IG(\alpha, \beta_j). Note that \beta_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.
verbose	a logical; TRUE to show iterations, FALSE otherwise.

Value

a named list containing

embed

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

stress

discrepancy between embedded and origianl data as a measure of error.

References

\insertRef

oh_bayesian_2001amaotai

Examples

## use simple example of iris dataset
data(iris) 
idata = as.matrix(iris[,1:4])

## run Bayesian MDS
#  let's run 10 iterations only.
iris.cmds = cmds(idata, ndim=2)
iris.bmds = bmds(idata, ndim=2, mc.iter=5, par.step=(2.38^2)) 

## extract coordinates and class information
cx = iris.cmds$embed # embedded coordinates of CMDS
bx = iris.bmds$embed #                         BMDS
icol = iris[,5]      # class information

## visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(2,1))
mc = paste0("CMDS with STRESS=",round(iris.cmds$stress,4))
mb = paste0("BMDS with STRESS=",round(iris.bmds$stress,4))
plot(cx, col=icol,pch=19,main=mc)
plot(bx, col=icol,pch=19,main=mb)
par(opar)

maotai documentation built on March 31, 2023, 6:48 p.m.