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.

## 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)
}
```