`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.

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

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 |

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 |

trained | A logical to indicate if the quantities for preprocessing have been estimated. |

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

res | An S4 |

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 |

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

id | A character string that is unique to this step to identify it. |

An updated version of `recipe`

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

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 dimRed and kernlab packages. If not installed, the step will stop with a prompt about installing these packages.

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 when `keep_original_cols = FALSE`

. 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`

, the
new names will be `kPC1`

- `kPC9`

. If `num_comp = 101`

, the names would be
`kPC001`

- `kPC101`

.

When you `tidy()`

this step, a tibble with column `terms`

(the selectors or variables selected) is returned.

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.

Other multivariate transformation steps:
`step_classdist()`

,
`step_depth()`

,
`step_geodist()`

,
`step_ica()`

,
`step_isomap()`

,
`step_kpca_rbf()`

,
`step_kpca()`

,
`step_mutate_at()`

,
`step_nnmf()`

,
`step_pca()`

,
`step_pls()`

,
`step_ratio()`

,
`step_spatialsign()`

```
library(modeldata)
data(biomass)
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())
if (require(dimRed) & require(kernlab)) {
kpca_estimates <- prep(kpca_trans, training = biomass_tr)
kpca_te <- bake(kpca_estimates, biomass_te)
rng <- extendrange(c(kpca_te$kPC1, kpca_te$kPC2))
plot(kpca_te$kPC1, kpca_te$kPC2,
xlim = rng, ylim = rng)
tidy(kpca_trans, number = 3)
tidy(kpca_estimates, number = 3)
}
#> # A tibble: 5 × 2
#> terms id
#> <chr> <chr>
#> 1 carbon kpca_poly_voo0Z
#> 2 hydrogen kpca_poly_voo0Z
#> 3 oxygen kpca_poly_voo0Z
#> 4 nitrogen kpca_poly_voo0Z
#> 5 sulfur kpca_poly_voo0Z
```