step_kpca
a specification of a recipe step that
will convert numeric data into one or more principal components
using a kernel basis expansion.
step_kpca( recipe, ..., role = "predictor", trained = FALSE, num_comp = 5, res = NULL, options = list(kernel = "rbfdot", kpar = list(sigma = 0.2)), prefix = "kPC", skip = FALSE, id = rand_id("kpca") ) # S3 method for step_kpca tidy(x, ...)
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

role  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. 
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 
options  A list of options to

prefix  A character string that will be the prefix to the resulting new variables. See notes below. 
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. 
x  A 
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).
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).
When performing kPCA, the kernel function (and any important
kernel parameters) must be chosen. The kernlab package is
used and the reference below discusses the types of kernels
available and their parameter(s). These specifications can be
made in the kernel
and kpar
slots of the
options
argument to step_kpca
.
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
.
Scholkopf, B., Smola, A., and Muller, K. (1997). Kernel principal component analysis. Lecture Notes in Computer Science, 1327, 583588.
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), 120.
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(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 x 2 #> terms id #> <chr> <chr> #> 1 carbon kpca_Qw9rI #> 2 hydrogen kpca_Qw9rI #> 3 oxygen kpca_Qw9rI #> 4 nitrogen kpca_Qw9rI #> 5 sulfur kpca_Qw9rI