do.sda: Semi-Supervised Discriminant Analysis

Description

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 $ℓ_{2}$ scheme via beta.

Usage

do.sda(X, label, ndim = 2, type = c("proportion", 0.1), alpha = 1,
  beta = 1)

Arguments

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 $(n \times n d i m)$ matrix whose rows are embedded observations.
trfinfo: a list containing information for out-of-sample prediction.
projection: a $(p \times n d i m)$ whose columns are basis for projection.

References

cai_semi-supervised_2007Rdimtools

Examples

Run this code

# NOT RUN {
## generate data of 3 types with clear difference
dt1  = aux.gensamples(n=33)-100
dt2  = aux.gensamples(n=33)
dt3  = aux.gensamples(n=33)+100

## merge the data and create a label correspondingly
X      = rbind(dt1,dt2,dt3)
label  = c(rep(1,33), rep(2,33), rep(3,33))

## 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

## compare true case with missing-label case
out1 = do.sda(X, label)
out2 = do.sda(X, label_missing)

## visualize
par(mfrow=c(1,2))
plot(out1$Y[,1], out1$Y[,2], main="true projection")
plot(out2$Y[,1], out2$Y[,2], main="20% missing labels")

# }