Kernel PCA Signal ExtractionSource:
step_kpca creates a specification of a recipe step that
will convert numeric data into one or more principal components
using a kernel basis expansion.
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.
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.
A logical to indicate if the quantities for preprocessing have been estimated.
The number of components to retain as new predictors. If
num_compis greater than the number of columns or the number of possible components, a smaller value will be used. If
num_comp = 0is set then no transformation is done and selected variables will stay unchanged.
A character string of variable names that will be populated elsewhere.
A list of options to
kernlab::kpca(). Defaults are set for the arguments
kparbut others can be passed in. Note that the arguments
featuresshould not be passed here (or at all).
A character string for the prefix of the resulting new variables. See notes below.
A logical to keep the original variables in the output. Defaults to
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 = TRUEas it may affect the computations for subsequent operations.
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.
When performing kPCA with
step_kpca(), you must choose the kernel
function (and any important kernel parameters). This step uses the
kernlab package; the reference below discusses the types of kernels
available and their parameter(s). These specifications can be made in the
kpar slots of the
options argument to
step_kpca_rbf() for a radial basis function kernel or
step_kpca_poly() for a polynomial kernel.
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
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
num_comp = 101, the names would be
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.
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(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_ntsLB tidy(kpca_estimates, number = 3) #> # A tibble: 5 × 2 #> terms id #> <chr> <chr> #> 1 carbon kpca_ntsLB #> 2 hydrogen kpca_ntsLB #> 3 oxygen kpca_ntsLB #> 4 nitrogen kpca_ntsLB #> 5 sulfur kpca_ntsLB