Modified Orthogonal Discriminant Projection (MODP) is a variant of Orthogonal Discriminant Projection (ODP).
Authors argue the assumption in modeling ODP's mechanism to reflect distance and class labeling seem unsound.
They propose a modified method to explore the intrinsic structure of original data and enhance
the classification ability.

```
do.modp(
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

Zhang S, Lei Y, Wu Y, Yang J (2011).
“Modified Orthogonal Discriminant Projection for Classification.”
*Neurocomputing*, **74**(17), 3690--3694.

## Examples

```
## 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 = rep(1:3, each=10)
## try different beta (scaling control) parameter
out1 = do.modp(X, label, beta=1)
out2 = do.modp(X, label, beta=10)
out3 = do.modp(X, label, beta=100)
## visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(out1$Y, main="MODP::beta=1")
plot(out2$Y, main="MODP::beta=10")
plot(out3$Y, main="MODP::beta=100")
par(opar)
```