Nonnegative Orthogonal Locality Preserving Projection (NOLPP) is a variant of OLPP where
projection vectors - or, basis for learned subspace - contain no negative values.

```
do.nolpp(
X,
ndim = 2,
type = c("proportion", 0.1),
preprocess = c("null", "center", "scale", "cscale", "decorrelate", "whiten"),
t = 1,
maxiter = 1000,
reltol = 1e-05
)
```

## Arguments

- X
an \((n\times p)\) matrix or data frame whose rows are observations.

- 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 "null". See also `aux.preprocess`

for more details.

- t
kernel bandwidth in \((0,\infty)\).

- maxiter
number of maximum iteraions allowed.

- reltol
stopping criterion for incremental relative error.

## 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

Zafeiriou S, Laskaris N (2010).
“Nonnegative Embeddings and Projections for Dimensionality Reduction and Information Visualization.”
In *2010 20th International Conference on Pattern Recognition*, 726--729.

## Examples

```
if (FALSE) {
## 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])
## use different kernel bandwidths with 20% connectivity
out1 = do.nolpp(X, type=c("proportion",0.5), t=0.01)
out2 = do.nolpp(X, type=c("proportion",0.5), t=0.1)
out3 = do.nolpp(X, type=c("proportion",0.5), t=1)
## visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(out1$Y, col=label, main="NOLPP::t=0.01")
plot(out2$Y, col=label, main="NOLPP::t=0.1")
plot(out3$Y, col=label, main="NOLPP::t=1")
par(opar)
}
```