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.preprocessfor 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.
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
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(out1$Y, pch=19, col=label, main="MMSD::C=0.01")
plot(out2$Y, pch=19, col=label, main="MMSD::C=1")
plot(out3$Y, pch=19, col=label, main="MMSD::C=100")
par(opar)