Multiple Maximum Scatter Difference (MMSD) is a supervised linear dimension reduction method. It is a variant of MSD in that discriminant vectors are orthonormal. Similar to MSD, it also does not suffer from rank deficiency issue of scatter matrix.

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

C

nonnegative balancing parameter for intra- and inter-class scatter.

## 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.

projection

a $$(p\times ndim)$$ whose columns are basis for projection.

## References

Fengxi Song, Zhang D, Dayong Mei, Zhongwei Guo (2007). “A Multiple Maximum Scatter Difference Discriminant Criterion for Facial Feature Extraction.” IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 37(6), 1599--1606.

Kisung You

## Examples

## generate data of 3 types with clear difference
set.seed(100)
dt1  = aux.gensamples(n=20)-50
dt2  = aux.gensamples(n=20)
dt3  = aux.gensamples(n=20)+50

## merge the data and create a label correspondingly
X      = rbind(dt1,dt2,dt3)
label  = rep(1:3, each=20)

## try different balancing parameter
out1 = do.mmsd(X, label, C=0.01)
out2 = do.mmsd(X, label, C=1)
out3 = do.mmsd(X, label, C=100)

## visualize
plot(out1$Y, pch=19, col=label, main="MMSD::C=0.01") plot(out2$Y, pch=19, col=label, main="MMSD::C=1")