Linear Quadratic Mutual Information

Linear Quadratic Mutual Information (LQMI) is a supervised linear dimension reduction method. Quadratic Mutual Information is an efficient nonparametric estimation method for Mutual Information for class labels not requiring class priors. For the KQMI formulation, LQMI is a linear equivalent.

do.lqmi(
  X,
  label,
  ndim = 2,
  preprocess = c("center", "scale", "cscale", "whiten", "decorrelate")
)

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.

preprocess

an additional option for preprocessing the data. Default is "center". See also aux.preprocess for more details.

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

Bouzas D, Arvanitopoulos N, Tefas A (2015). “Graph Embedded Nonparametric Mutual Information for Supervised Dimensionality Reduction.” IEEE Transactions on Neural Networks and Learning Systems, 26(5), 951--963.

See also

do.kqmi

Author

Kisung You

Examples

## 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])

## compare against LDA
out1 = do.lda(X, label)
out2 = do.lqmi(X, label)

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

par(opar)