`do.lpp`

is a linear approximation to Laplacian Eigenmaps. More precisely,
it aims at finding a linear approximation to the eigenfunctions of the Laplace-Beltrami
operator on the graph-approximated data manifold.

```
do.lpp(
X,
ndim = 2,
type = c("proportion", 0.1),
symmetric = c("union", "intersect", "asymmetric"),
preprocess = c("center", "scale", "cscale", "whiten", "decorrelate"),
t = 1
)
```

## 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.

- symmetric
one of `"intersect"`

, `"union"`

or `"asymmetric"`

is supported. Default is `"union"`

.
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.

- t
bandwidth for heat kernel 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

He X (2005).
*Locality Preserving Projections*.
PhD Thesis, University of Chicago, Chicago, IL, USA.

## Examples

```
## use iris dataset
data(iris)
set.seed(100)
subid <- sample(1:150, 50)
X <- as.matrix(iris[subid,1:4])
lab <- as.factor(iris[subid,5])
## try different kernel bandwidths
out1 <- do.lpp(X, t=0.1)
out2 <- do.lpp(X, t=1)
out3 <- do.lpp(X, t=10)
## Visualize three different projections
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(out1$Y, col=lab, pch=19, main="LPP::bandwidth=0.1")
plot(out2$Y, col=lab, pch=19, main="LPP::bandwidth=1")
plot(out3$Y, col=lab, pch=19, main="LPP::bandwidth=10")
par(opar)
```