step_kpca {recipes} | R Documentation |
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 = 5, res = NULL, options = list(kernel = "rbfdot", kpar = list(sigma = 0.2)), prefix = "kPC")
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 |
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. |
Kernel principal component analysis (kPCA) is an extension 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.
As with ordinary PCA, it is important to standardized 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
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 < 10
, their names will be
kPC1
- kPC9
. If num = 101
, the names would be
kPC001
- kPC101
.
An updated version of recipe
with the
new step added to the sequence of existing steps (if any).
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
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_center(all_predictors()) %>% step_scale(all_predictors()) %>% step_kpca(all_predictors()) 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)