Maximum Margin Projection

Maximum Margin Projection (MMP) is a supervised linear method that maximizes the margin between positive and negative examples at each local neighborhood based on same- and different-class neighborhoods depending on class labels.

do.mmp(
  X,
  label,
  ndim = 2,
  preprocess = c("center", "scale", "cscale", "decorrelate", "whiten"),
  numk = max(ceiling(nrow(X)/10), 2),
  alpha = 0.5,
  gamma = 50
)

Arguments

X

an \((n\times p)\) matrix or data frame whose rows are observations.

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.

numk

the number of neighboring points.

alpha

balancing parameter in \([0,1]\).

gamma

weight for same-label data points with large magnitude.

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

Xiaofei He, Deng Cai, Jiawei Han (2008). “Learning a Maximum Margin Subspace for Image Retrieval.” IEEE Transactions on Knowledge and Data Engineering, 20(2), 189--201.

Author

Kisung You

Examples

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

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

## copy a label and let 20% of elements be missing
nlabel = length(label)
nmissing = round(nlabel*0.20)
label_missing = label
label_missing[sample(1:nlabel, nmissing)]=NA

## compare with PCA case for full-label case
## for missing label case from MMP computation
out1 = do.pca(X, ndim=2)
out2 = do.mmp(X, label_missing, numk=10)

## visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,2))
plot(out1$Y, col=label, main="PCA projection")
plot(out2$Y, col=label, main="20% missing labels")

par(opar)