step_kpca_rbf a specification of a recipe step that will convert numeric data into one or more principal components using a radial basis function kernel basis expansion.

step_kpca_rbf(
recipe,
...,
role = "predictor",
trained = FALSE,
num_comp = 5,
res = NULL,
sigma = 0.2,
prefix = "kPC",
skip = FALSE,
id = rand_id("kpca_rbf")
)

# S3 method for step_kpca_rbf
tidy(x, ...)

## 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 which variables will be used to compute the components. See selections() for more details. For the tidy method, these are not currently used. For model terms created by this step, what analysis role should they be assigned? By default, the function assumes that the new principal component columns created by the original variables will be used as predictors in a model. A logical to indicate if the quantities for preprocessing have been estimated. The number of PCA 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. An S4 kernlab::kpca() object is stored here once this preprocessing step has be trained by prep.recipe(). A numeric value for the radial basis function parameter. A character string that will be the prefix to the resulting new variables. See notes below. A logical. Should the step be skipped when the recipe is baked by bake.recipe()? While all operations are baked when prep.recipe() 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 A character string that is unique to this step to identify it. A step_kpca_rbf object

## Value

An updated version of recipe with the new step added to the sequence of existing steps (if any). For the tidy method, a tibble with columns terms (the selectors or variables selected).

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

As with ordinary PCA, it is important to standardize the variables prior to running PCA (step_center and step_scale 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 kPC001 - kPC101.

## 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.

step_pca() step_ica() step_isomap() recipe() prep.recipe() bake.recipe()

## Examples

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_predictors()) %>%
step_normalize(all_predictors()) %>%
step_kpca_rbf(all_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)
}
#> 2020-10-19 00:09:02: Calculating kernel PCA#> 2020-10-19 00:09:02: Trying to calculate reverse#> 2020-10-19 00:09:02: DONE#> # A tibble: 5 x 2
#>   terms    id
#>   <chr>    <chr>
#> 1 carbon   kpca_rbf_68zye
#> 2 hydrogen kpca_rbf_68zye
#> 3 oxygen   kpca_rbf_68zye
#> 4 nitrogen kpca_rbf_68zye
#> 5 sulfur   kpca_rbf_68zye