do.mmc: Maximum Margin Criterion

Description

Maximum Margin Criterion (MMC) is a linear supervised dimension reduction method that maximizes average margin between classes. The cost function is defined as $t r a c e (S_{b} - S_{w})$ where $S_{b}$ is an overall variance of class mean vectors, and $S_{w}$ refers to spread of every class. Note that Principal Component Analysis (PCA) maximizes total scatter, $S_{t} = S_{b} + S_{w}$ .

Usage

do.mmc(
  X,
  label,
  ndim = 2,
  preprocess = c("center", "scale", "cscale", "decorrelate", "whiten")
)

Arguments

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.

Value

a named list containing

Y: an $(n \times n d i m)$ matrix whose rows are embedded observations.
trfinfo: a list containing information for out-of-sample prediction.
projection: a $(p \times n d i m)$ whose columns are basis for projection.

References

li_efficient_2006Rdimtools

Examples

Run this code

# NOT RUN {
## generate 3 different groups of data X and label vector
x1 = matrix(rnorm(4*10), nrow=10)-20
x2 = matrix(rnorm(4*10), nrow=10)
x3 = matrix(rnorm(4*10), nrow=10)+20
X  = rbind(x1, x2, x3)
label = c(rep(1,10), rep(2,10), rep(3,10))

## perform MVP with different preprocessings
out1 = do.mmc(X, label, ndim=2)
out2 = do.mmc(X, label, ndim=2, preprocess="decorrelate")

## visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,2))
plot(out1$Y, main="MMC::centering")
plot(out2$Y, main="MMC::decorrelating")
par(opar)

# }