Kernel Quadratic Mutual Information

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.

See also

do.lqmi

Author

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
opar = par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(out1$Y, col=label, main="KQMI::t=0.01")
plot(out2$Y, col=label, main="KQMI::t=1")
plot(out3$Y, col=label, main="KQMI::t=100")
par(opar)
}