Kernel Quadratic Mutual Information (KQMI) 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. The method re-states the estimation procedure in terms of kernel objective in the graph embedding framework.

do.kqmi(
X,
label,
ndim = 2,
preprocess = c("center", "scale", "cscale", "whiten", "decorrelate"),
t = 10
)

## 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.

t

bandwidth parameter for heat kernel 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

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.

do.lqmi

Kisung You

## Examples

if (FALSE) {
## generate 3 different groups of data X and label vector
x1 = matrix(rnorm(4*10), nrow=10)-20
x2 = matrix(rnorm(4*10), nrow=10)
x3 = matrix(rnorm(4*10), nrow=10)+20
X  = rbind(x1, x2, x3)
label = c(rep(1,10), rep(2,10), rep(3,10))

## try different kernel bandwidths
out1 = do.kqmi(X, label, t=0.01)
out2 = do.kqmi(X, label, t=1)
out3 = do.kqmi(X, label, t=100)

## visualize
plot(out1$Y, col=label, main="KQMI::t=0.01") plot(out2$Y, col=label, main="KQMI::t=1")