Semi-Supervised Discriminant Analysis

Semi-Supervised Discriminant Analysis (SDA) is a linear dimension reduction method when label is partially missing, i.e., semi-supervised. The labeled data points are used to maximize the separability between classes while the unlabeled ones to estimate the intrinsic structure of the data. Regularization in case of rank-deficient case is also supported via an \(\ell_2\) scheme via beta.

do.sda(X, label, ndim = 2, type = c("proportion", 0.1), alpha = 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.

alpha

balancing parameter between model complexity and empirical loss.

beta

Tikhonov regularization parameter.

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

Cai D, He X, Han J (2007). “Semi-Supervised Discriminant Analysis.” In 2007 IEEE 11th International Conference on Computer Vision, 1--7.

Author

Kisung You

Examples

## use iris data
data(iris)
X     = as.matrix(iris[,1:4])
label = as.integer(iris$Species)

## 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 true case with missing-label case
out1 = do.sda(X, label)
#> * Semi-Supervised Learning : there is no missing labels. Consider using Supervised methods.
out2 = do.sda(X, label_missing)

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

par(opar)