Truncated PCA Signal Extraction — step_pca

step_pca_truncated() creates a specification of a recipe step that will convert numeric data into one or more principal components. It is truncated as it only calculates the number of components it is asked instead of all of them as is done in recipes::step_pca().

Usage

step_pca_truncated(
  recipe,
  ...,
  role = "predictor",
  trained = FALSE,
  num_comp = 5,
  options = list(),
  res = NULL,
  columns = NULL,
  prefix = "PC",
  keep_original_cols = FALSE,
  skip = FALSE,
  id = rand_id("pca_truncated")
)

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 variables for this step. See selections() for more details.
role: 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.
trained: A logical to indicate if the quantities for preprocessing have been estimated.
num_comp: The number of 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. If num_comp = 0 is set then no transformation is done and selected variables will stay unchanged, regardless of the value of keep_original_cols.
options: A list of options to the default method for irlba::prcomp_irlba(). Argument defaults are set to retx = FALSE, center = FALSE, scale. = FALSE, and tol = NULL. Note that the argument x should not be passed here (or at all).
res: The irlba::prcomp_irlba() object is stored here once this preprocessing step has be trained by prep().
columns: A character string of the selected variable names. This field is a placeholder and will be populated once prep() is used.
prefix: A character string for the prefix of the resulting new variables. See notes below.
keep_original_cols: A logical to keep the original variables in the output. Defaults to FALSE.
skip: 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 = TRUE as it may affect the computations for subsequent operations.
id: A character string that is unique to this step to identify it.

Value

An updated version of recipe with the new step added to the sequence of any existing operations.

Details

Principal component analysis (PCA) is a transformation of a group of variables that produces a new set of artificial features or components. These components are designed to capture the maximum amount of information (i.e. variance) in the original variables. Also, the components are statistically independent from one another. This means that they can be used to combat large inter-variables correlations in a data set.

It is advisable to standardize the variables prior to running PCA. Here, each variable will be centered and scaled prior to the PCA calculation. This can be changed using the options argument or by using step_center() and step_scale().

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 PC1 - PC9. If num_comp = 101, the names would be PC1 - PC101.

Tidying

When you tidy() this step two things can happen depending the type argument. If type = "coef" a tibble returned with 4 columns terms, value, component , and id:

terms: character, the selectors or variables selected
value: numeric, variable loading
component: character, principle component
id: character, id of this step

If type = "variance" a tibble returned with 4 columns terms, value, component , and id:

terms: character, type of variance
value: numeric, value of the variance
component: integer, principle component
id: character, id of this step

Tuning Parameters

This step has 1 tuning parameters:

num_comp: # Components (type: integer, default: 5)

Case weights

This step performs an unsupervised operation that can utilize case weights. As a result, case weights are only used with frequency weights. For more information, see the documentation in case_weights and the examples on tidymodels.org.

References

Jolliffe, I. T. (2010). Principal Component Analysis. Springer.

Examples

rec <- recipe(~., data = mtcars)
pca_trans <- rec %>%
  step_normalize(all_numeric()) %>%
  step_pca_truncated(all_numeric(), num_comp = 2)
pca_estimates <- prep(pca_trans, training = mtcars)
pca_data <- bake(pca_estimates, mtcars)

rng <- extendrange(c(pca_data$PC1, pca_data$PC2))
plot(pca_data$PC1, pca_data$PC2,
  xlim = rng, ylim = rng
)


tidy(pca_trans, number = 2)
#> # A tibble: 1 × 4
#>   terms         value component id                 
#>   <chr>         <dbl> <chr>     <chr>              
#> 1 all_numeric()    NA NA        pca_truncated_AGa8C
tidy(pca_estimates, number = 2)
#> # A tibble: 22 × 4
#>    terms  value component id                 
#>    <chr>  <dbl> <chr>     <chr>              
#>  1 mpg    0.363 PC1       pca_truncated_AGa8C
#>  2 cyl   -0.374 PC1       pca_truncated_AGa8C
#>  3 disp  -0.368 PC1       pca_truncated_AGa8C
#>  4 hp    -0.330 PC1       pca_truncated_AGa8C
#>  5 drat   0.294 PC1       pca_truncated_AGa8C
#>  6 wt    -0.346 PC1       pca_truncated_AGa8C
#>  7 qsec   0.200 PC1       pca_truncated_AGa8C
#>  8 vs     0.307 PC1       pca_truncated_AGa8C
#>  9 am     0.235 PC1       pca_truncated_AGa8C
#> 10 gear   0.207 PC1       pca_truncated_AGa8C
#> # ℹ 12 more rows