`step_kpca_poly()`

creates a *specification* of a recipe step that will
convert numeric data into one or more principal components using a polynomial
kernel basis expansion.

## Usage

```
step_kpca_poly(
recipe,
...,
role = "predictor",
trained = FALSE,
num_comp = 5,
res = NULL,
columns = NULL,
degree = 2,
scale_factor = 1,
offset = 1,
prefix = "kPC",
keep_original_cols = FALSE,
skip = FALSE,
id = rand_id("kpca_poly")
)
```

## Arguments

- recipe
A recipe object. The step will be added to the sequence of operations for this recipe.

- ...
One or more selector functions to choose variables for this step. See

`selections()`

for more details.- role
For model terms created by this step, what analysis role should they be assigned? By default, the new columns created by this step from the original variables will be used as

*predictors*in a model.- trained
A logical to indicate if the quantities for preprocessing have been estimated.

- num_comp
The number of components to retain as new predictors. If

`num_comp`

is greater than the number of columns or the number of possible components, a smaller value will be used. If`num_comp = 0`

is set then no transformation is done and selected variables will stay unchanged, regardless of the value of`keep_original_cols`

.- res
An S4

`kernlab::kpca()`

object is stored here once this preprocessing step has be trained by`prep()`

.- columns
A character string of the selected variable names. This field is a placeholder and will be populated once

`prep()`

is used.- degree, scale_factor, offset
Numeric values for the polynomial kernel function.

- prefix
A character string for the prefix of the resulting new variables. See notes below.

- keep_original_cols
A logical to keep the original variables in the output. Defaults to

`FALSE`

.- skip
A logical. Should the step be skipped when the recipe is baked by

`bake()`

? While all operations are baked when`prep()`

is run, some operations may not be able to be conducted on new data (e.g. processing the outcome variable(s)). Care should be taken when using`skip = TRUE`

as it may affect the computations for subsequent operations.- id
A character string that is unique to this step to identify it.

## Value

An updated version of `recipe`

with the new step added to the
sequence of any existing operations.

## Details

Kernel principal component analysis (kPCA) is an extension of a PCA analysis that conducts the calculations in a broader dimensionality defined by a kernel function. For example, if a quadratic kernel function were used, each variable would be represented by its original values as well as its square. This nonlinear mapping is used during the PCA analysis and can potentially help find better representations of the original data.

This step requires the kernlab package. If not installed, the step will stop with a prompt about installing the package.

As with ordinary PCA, it is important to center and scale the variables
prior to computing PCA components (`step_normalize()`

can be used for
this purpose).

The argument `num_comp`

controls the number of components that will be retained
(the original variables that are used to derive the components are removed from
the data). The new components will have names that begin with `prefix`

and a
sequence of numbers. The variable names are padded with zeros. For example, if
`num_comp < 10`

, their names will be `kPC1`

- `kPC9`

. If `num_comp = 101`

,
the names would be `kPC1`

- `kPC101`

.

## tidy() results

When you `tidy()`

this step, a tibble with column
`terms`

(the selectors or variables selected) is returned.

## Tuning Parameters

This step has 4 tuning parameters:

`num_comp`

: # Components (type: integer, default: 5)`degree`

: Polynomial Degree (type: double, default: 2)`scale_factor`

: Scale Factor (type: double, default: 1)`offset`

: Offset (type: double, default: 1)

## Tidying

When you `tidy()`

this step, a tibble is returned with
columns `terms`

and `id`

:

- terms
character, the selectors or variables selected

- id
character, id of this step

## References

Scholkopf, B., Smola, A., and Muller, K. (1997).
Kernel principal component analysis. *Lecture Notes in
Computer Science*, 1327, 583-588.

Karatzoglou, K., Smola, A., Hornik, K., and Zeileis, A. (2004).
kernlab - An S4 package for kernel methods in R. *Journal
of Statistical Software*, 11(1), 1-20.

## See also

Other multivariate transformation steps:
`step_classdist_shrunken()`

,
`step_classdist()`

,
`step_depth()`

,
`step_geodist()`

,
`step_ica()`

,
`step_isomap()`

,
`step_kpca_rbf()`

,
`step_kpca()`

,
`step_mutate_at()`

,
`step_nnmf_sparse()`

,
`step_nnmf()`

,
`step_pca()`

,
`step_pls()`

,
`step_ratio()`

,
`step_spatialsign()`

## Examples

```
library(ggplot2)
data(biomass, package = "modeldata")
biomass_tr <- biomass[biomass$dataset == "Training", ]
biomass_te <- biomass[biomass$dataset == "Testing", ]
rec <- recipe(
HHV ~ carbon + hydrogen + oxygen + nitrogen + sulfur,
data = biomass_tr
)
kpca_trans <- rec %>%
step_YeoJohnson(all_numeric_predictors()) %>%
step_normalize(all_numeric_predictors()) %>%
step_kpca_poly(all_numeric_predictors())
kpca_estimates <- prep(kpca_trans, training = biomass_tr)
kpca_te <- bake(kpca_estimates, biomass_te)
ggplot(kpca_te, aes(x = kPC1, y = kPC2)) +
geom_point() +
coord_equal()
tidy(kpca_trans, number = 3)
#> # A tibble: 1 × 2
#> terms id
#> <chr> <chr>
#> 1 all_numeric_predictors() kpca_poly_Qw9rI
tidy(kpca_estimates, number = 3)
#> # A tibble: 5 × 2
#> terms id
#> <chr> <chr>
#> 1 carbon kpca_poly_Qw9rI
#> 2 hydrogen kpca_poly_Qw9rI
#> 3 oxygen kpca_poly_Qw9rI
#> 4 nitrogen kpca_poly_Qw9rI
#> 5 sulfur kpca_poly_Qw9rI
```