Kernel Maximum Margin Criterion

Kernel Maximum Margin Criterion (KMMC) is a nonlinear variant of MMC method using kernel trick. For computational simplicity, only the gaussian kernel is used with bandwidth parameter t.

do.kmmc(
  X,
  label,
  ndim = 2,
  preprocess = c("center", "decorrelate", "whiten"),
  t = 1
)

Arguments

X

an \((n\times p)\) matrix or data frame whose rows are observations and columns represent independent variables.

label

a length-\(n\) vector of data class labels.

ndim

an integer-valued target dimension.

preprocess

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

t

bandwidth parameter for heat kernel in \((0,\infty)\).

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

Li H, Jiang T, Zhang K (2006). “Efficient and Robust Feature Extraction by Maximum Margin Criterion.” IEEE Transactions on Neural Networks, 17(1), 157--165.

See also

do.mmc

Author

Kisung You

Examples

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

## perform MVP with different preprocessings
out1 = do.kmmc(X, label, t=0.1)
out2 = do.kmmc(X, label, t=1.0)
out3 = do.kmmc(X, label, t=10.0)

## visualize
opar = par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(out1$Y, pch=19, col=label, main="bandwidth=0.1")
plot(out2$Y, pch=19, col=label, main="bandwidth=1")
plot(out3$Y, pch=19, col=label, main="bandwidth=10.0")

par(opar)
# }