Orthogonal Discriminant Projection (ODP) is a linear dimension reduction method with label information, i.e., *supervised*.
The method maximizes weighted difference between local and non-local scatter while local information is also preserved by
constructing a neighborhood graph.

```
do.odp(
X,
label,
ndim = 2,
preprocess = c("center", "scale", "cscale", "decorrelate", "whiten"),
type = c("proportion", 0.1),
symmetric = c("union", "intersect", "asymmetric"),
alpha = 0.5,
beta = 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.

- type
a vector of neighborhood graph construction. Following types are supported;
`c("knn",k)`

, `c("enn",radius)`

, and `c("proportion",ratio)`

.
Default is `c("proportion",0.1)`

, connecting about 1/10 of nearest data points
among all data points. See also `aux.graphnbd`

for more details.

- symmetric
one of `"intersect"`

, `"union"`

or `"asymmetric"`

is supported. Default is `"union"`

. See also `aux.graphnbd`

for more details.

- alpha
balancing parameter of non-local and local scatter in \([0,1]\).

- beta
scaling control parameter for distant pairs of data in \((0,\infty)\).

## Value

a named list containing

- Y
an \((n\times ndim)\) matrix whose rows are embedded observations.

- projection
a \((p\times ndim)\) whose columns are basis for projection.

- trfinfo
a list containing information for out-of-sample prediction.

## References

Li B, Wang C, Huang D (2009).
“Supervised Feature Extraction Based on Orthogonal Discriminant Projection.”
*Neurocomputing*, **73**(1-3), 191--196.

## 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])
## try different beta (scaling control) parameter
out1 = do.odp(X, label, beta=1)
out2 = do.odp(X, label, beta=10)
out3 = do.odp(X, label, beta=100)
## visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(out1$Y, col=label, pch=19, main="ODP::beta=1")
plot(out2$Y, col=label, pch=19, main="ODP::beta=10")
plot(out3$Y, col=label, pch=19, main="ODP::beta=100")
par(opar)
```