Rdimtools (version 1.1.2)

do.rlda: Regularized Linear Discriminant Analysis

Description

In small sample case, Linear Discriminant Analysis (LDA) may suffer from rank deficiency issue. Applied mathematics has used Tikhonov regularization - also known as \(\ell_2\) regularization/shrinkage - to adjust linear operator. Regularized Linear Discriminant Analysis (RLDA) adopts such idea to stabilize eigendecomposition in LDA formulation.

Usage

do.rlda(X, label, ndim = 2, alpha = 1)

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.

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.

alpha

Tikhonow regularization parameter.

Author

Kisung You

References

friedman_regularized_1989Rdimtools

Examples

if (FALSE) {
## use iris data
data(iris)
set.seed(100)
subid = sample(1:150, 50)
X     = as.matrix(iris[subid,1:4])
label = as.factor(iris[subid,5])

## try different regularization parameters
out1 <- do.rlda(X, label, alpha=0.001)
out2 <- do.rlda(X, label, alpha=0.01)
out3 <- do.rlda(X, label, alpha=100)

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