Maximum Scatter Difference (MSD) is a supervised linear dimension reduction method. The basic idea of MSD is to use additive cost function rather than multiplicative trace ratio criterion that was adopted by LDA. Due to such formulation, it can neglect sample-sample-size problem from rank-deficiency of between-class variance matrix.

do.msd(
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 variance.

## 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

Song F, Zhang D, Chen Q, Wang J (2007). “Face Recognition Based on a Novel Linear Discriminant Criterion.” Pattern Analysis and Applications, 10(3), 165--174.

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.msd(X, label, C=0.01)
out2 = do.msd(X, label, C=1)
out3 = do.msd(X, label, C=100)

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