Semi-Supervised Adaptive Maximum Margin Criterion

Semi-Supervised Adaptive Maximum Margin Criterion (SAMMC) is a semi-supervised variant of AMMC by making use of both labeled and unlabeled data.

do.sammc(
  X,
  label,
  ndim = 2,
  type = c("proportion", 0.1),
  preprocess = c("center", "scale", "cscale", "decorrelate", "whiten"),
  a = 1,
  b = 1,
  lambda = 1,
  beta = 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.
type: a vector of neighborhood graph construction. Following types are supported; c("knn",k), c("enn",radius), and c("proportion",ratio). Default is c("proportion",0.1), connecting about 1/10 of nearest data points among all data points. See also aux.graphnbd for more details.
preprocess: an additional option for preprocessing the data. Default is "center". See also aux.preprocess for more details.
a: tuning parameter for between-class weight in \([0,\infty)\).
b: tuning parameter for within-class weight in \([0,\infty)\).
lambda: balance parameter for between-class and within-class scatter matrices in \((0,\infty)\).
beta: balance parameter for within-class scatter of the labeled data and consistency of the whole data in \((0,\infty)\).

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

Lu J, Tan Y (2011). “Adaptive Maximum Margin Criterion for Image Classification.” In 2011 IEEE International Conference on Multimedia and Expo, 1--6.

Author

Kisung You

Examples

## generate data of 3 types with clear difference
set.seed(100)
dt1  = aux.gensamples(n=33)-50
dt2  = aux.gensamples(n=33)
dt3  = aux.gensamples(n=33)+50

## merge the data and create a label correspondingly
X      = rbind(dt1,dt2,dt3)
label  = rep(1:3, each=33)

## 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

## try different balancing
out1 = do.sammc(X, label_missing, beta=0.1)
out2 = do.sammc(X, label_missing, beta=1)
out3 = do.sammc(X, label_missing, beta=10)

## visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(out1$Y, pch=19, col=label, main="SAMMC::beta=0.1")
plot(out2$Y, pch=19, col=label, main="SAMMC::beta=1")
plot(out3$Y, pch=19, col=label, main="SAMMC::beta=10")

par(opar)