Orthogonal Neighborhood Preserving Projection (ONPP) is an unsupervised linear dimension reduction method.
It constructs a weighted data graph from LLE method. Also, it develops LPP method by preserving
the structure of local neighborhoods.

```
do.onpp(
X,
ndim = 2,
type = c("proportion", 0.1),
preprocess = c("center", "scale", "cscale", "decorrelate", "whiten")
)
```

## Arguments

- X
an \((n\times p)\) matrix or data frame whose rows are observations
and columns represent independent variables.

- ndim
an integer-valued target dimension.

- 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.

- preprocess
an additional option for preprocessing the data.
Default is "center". See also `aux.preprocess`

for more details.

## 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

Kokiopoulou E, Saad Y (2007).
“Orthogonal Neighborhood Preserving Projections: A Projection-Based Dimensionality Reduction Technique.”
*IEEE Transactions on Pattern Analysis and Machine Intelligence*, **29**(12), 2143--2156.

## 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 numbers for neighborhood size
out1 = do.onpp(X, type=c("proportion",0.10))
out2 = do.onpp(X, type=c("proportion",0.25))
out3 = do.onpp(X, type=c("proportion",0.50))
## visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(out1$Y, pch=19, col=label, main="ONPP::10% connectivity")
plot(out2$Y, pch=19, col=label, main="ONPP::25% connectivity")
plot(out3$Y, pch=19, col=label, main="ONPP::50% connectivity")
par(opar)
```