S4 Class implementing PCA with L1 error.

## Details

PCA transforms the data so that the L2 reconstruction error is minimized or the variance of the projected data is maximized. This is sensitive to outliers, L1 PCA minimizes the L1 reconstruction error or maximizes the sum of the L1 norm of the projected observations.

## Slots

`fun`

A function that does the embedding and returns a dimRedResult object.

`stdpars`

The standard parameters for the function.

## General usage

Dimensionality reduction methods are S4 Classes that either be used
directly, in which case they have to be initialized and a full
list with parameters has to be handed to the `@fun()`

slot, or the method name be passed to the embed function and
parameters can be given to the `...`

, in which case
missing parameters will be replaced by the ones in the
`@stdpars`

.

## Parameters

PCA can take the following parameters:

- ndim
The number of output dimensions.

- center
logical, should the data be centered, defaults to

`TRUE`

.- scale.
logical, should the data be scaled, defaults to

`FALSE`

.- fun
character or function, the method to apply, see the

`pcaL1`

package- ...
other parameters for

`fun`

## Implementation

Wraps around the different methods is the `pcaL1`

package. Because PCA
can be reduced to a simple rotation, forward and backward projection
functions are supplied.

## References

Park, Y.W., Klabjan, D., 2016. Iteratively Reweighted Least Squares Algorithms for L1-Norm Principal Component Analysis, in: Data Mining (ICDM), 2016 IEEE 16th International Conference On. IEEE, pp. 430-438.

## See also

Other dimensionality reduction methods:
`AutoEncoder-class`

,
`DRR-class`

,
`DiffusionMaps-class`

,
`DrL-class`

,
`FastICA-class`

,
`FruchtermanReingold-class`

,
`HLLE-class`

,
`Isomap-class`

,
`KamadaKawai-class`

,
`MDS-class`

,
`NNMF-class`

,
`PCA-class`

,
`UMAP-class`

,
`dimRedMethod-class`

,
`dimRedMethodList()`

,
`kPCA-class`

,
`nMDS-class`

,
`tSNE-class`

## Examples

```
if(requireNamespace("pcaL1", quietly = TRUE)) {
dat <- loadDataSet("Iris")
emb <- embed(dat, "PCA_L1")
plot(emb, type = "2vars")
plot(inverse(emb, getData(getDimRedData((emb)))), type = "3vars")
}
```