R: Kernel PCA Signal Extraction

step_kpca {recipes} | R Documentation

## Kernel PCA Signal Extraction

### Description

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

### Usage

    step_kpca(recipe, ..., role = "predictor", trained = FALSE, num = 5,
      res = NULL, options = list(kernel = "rbfdot", kpar = list(sigma = 0.2)),
      prefix = "kPC", skip = FALSE)

    ## S3 method for class 'step_kpca'
    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.
`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 `num` is greater than the number of columns or the number of possible components, a smaller value will be used.
`res` | An S4 `kernlab::kpca()` object is stored here once this preprocessing step has be trained by `prep.recipe()`.
`options` | A list of options to `kernlab::kpca()`. Defaults are set for the arguments `kernel` and `kpar` but others can be passed in. Note that the arguments `x` and `features` should not be passed here (or at all).
`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 `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
`x` | A `step_kpca` object

### Details

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`.

### 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).

### 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.

### See Also

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

### Examples

    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)

    tidy(kpca_trans, number = 4)
    tidy(kpca_estimates, number = 4)

[Package recipes version 0.1.2 Index]