Conventional LTSA method relies on PCA for approximating local tangent spaces.
Improved LTSA (ILTSA) provides a remedy that can efficiently recover the geometric
structure of data manifolds even when data are sparse or non-uniformly distributed.

```
do.iltsa(
X,
ndim = 2,
type = c("proportion", 0.25),
symmetric = c("union", "intersect", "asymmetric"),
preprocess = c("center", "scale", "cscale", "decorrelate", "whiten"),
t = 10
)
```

## 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.

- 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
heat kernel bandwidth parameter in \((0,\infty)\).

## 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.

## References

Zhang P, Qiao H, Zhang B (2011).
“An Improved Local Tangent Space Alignment Method for Manifold Learning.”
*Pattern Recognition Letters*, **32**(2), 181--189.

## Examples

```
# \donttest{
## load 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 bandwidth size
out1 <- do.iltsa(X, t=1)
out2 <- do.iltsa(X, t=10)
out3 <- do.iltsa(X, t=100)
## Visualize two comparisons
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(out1$Y, pch=19, col=label, main="ILTSA::t=1")
plot(out2$Y, pch=19, col=label, main="ILTSA::t=10")
plot(out3$Y, pch=19, col=label, main="ILTSA::t=100")
par(opar)
# }
```