PCA signal extraction

step_pca() creates a specification of a recipe step that will convert numeric variables into one or more principal components.

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

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.
threshold: A fraction of the total variance that should be covered by the components. For example, threshold = .75 means that step_pca() should generate enough components to capture 75 percent of the variability in the variables. Note: using this argument will override and reset any value given to num_comp.
options: A list of options to the default method for stats::prcomp(). 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 stats::prcomp.default() 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.

Alternatively, threshold can be used to determine the number of components that are required to capture a specified fraction of the total variance in the variables.

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 2 tuning parameters:

num_comp: # Components (type: integer, default: 5)
threshold: Threshold (type: double, default: NA)

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 = USArrests)
pca_trans <- rec |>
  step_normalize(all_numeric()) |>
  step_pca(all_numeric(), num_comp = 3)
pca_estimates <- prep(pca_trans, training = USArrests)
pca_data <- bake(pca_estimates, USArrests)

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


with_thresh <- rec |>
  step_normalize(all_numeric()) |>
  step_pca(all_numeric(), threshold = .99)
with_thresh <- prep(with_thresh, training = USArrests)
bake(with_thresh, USArrests)
#> # A tibble: 50 × 4
#>        PC1     PC2     PC3      PC4
#>      <dbl>   <dbl>   <dbl>    <dbl>
#>  1 -0.976  -1.12    0.440   0.155  
#>  2 -1.93   -1.06   -2.02   -0.434  
#>  3 -1.75    0.738  -0.0542 -0.826  
#>  4  0.140  -1.11   -0.113  -0.181  
#>  5 -2.50    1.53   -0.593  -0.339  
#>  6 -1.50    0.978  -1.08    0.00145
#>  7  1.34    1.08    0.637  -0.117  
#>  8 -0.0472  0.322   0.711  -0.873  
#>  9 -2.98   -0.0388  0.571  -0.0953 
#> 10 -1.62   -1.27    0.339   1.07   
#> # ℹ 40 more rows

tidy(pca_trans, number = 2)
#> # A tibble: 1 × 4
#>   terms         value component id       
#>   <chr>         <dbl> <chr>     <chr>    
#> 1 all_numeric()    NA NA        pca_Esd0U
tidy(pca_estimates, number = 2)
#> # A tibble: 16 × 4
#>    terms      value component id       
#>    <chr>      <dbl> <chr>     <chr>    
#>  1 Murder   -0.536  PC1       pca_Esd0U
#>  2 Assault  -0.583  PC1       pca_Esd0U
#>  3 UrbanPop -0.278  PC1       pca_Esd0U
#>  4 Rape     -0.543  PC1       pca_Esd0U
#>  5 Murder   -0.418  PC2       pca_Esd0U
#>  6 Assault  -0.188  PC2       pca_Esd0U
#>  7 UrbanPop  0.873  PC2       pca_Esd0U
#>  8 Rape      0.167  PC2       pca_Esd0U
#>  9 Murder    0.341  PC3       pca_Esd0U
#> 10 Assault   0.268  PC3       pca_Esd0U
#> 11 UrbanPop  0.378  PC3       pca_Esd0U
#> 12 Rape     -0.818  PC3       pca_Esd0U
#> 13 Murder    0.649  PC4       pca_Esd0U
#> 14 Assault  -0.743  PC4       pca_Esd0U
#> 15 UrbanPop  0.134  PC4       pca_Esd0U
#> 16 Rape      0.0890 PC4       pca_Esd0U
tidy(pca_estimates, number = 2, type = "variance")
#> # A tibble: 16 × 4
#>    terms                         value component id       
#>    <chr>                         <dbl>     <int> <chr>    
#>  1 variance                      2.48          1 pca_Esd0U
#>  2 variance                      0.990         2 pca_Esd0U
#>  3 variance                      0.357         3 pca_Esd0U
#>  4 variance                      0.173         4 pca_Esd0U
#>  5 cumulative variance           2.48          1 pca_Esd0U
#>  6 cumulative variance           3.47          2 pca_Esd0U
#>  7 cumulative variance           3.83          3 pca_Esd0U
#>  8 cumulative variance           4             4 pca_Esd0U
#>  9 percent variance             62.0           1 pca_Esd0U
#> 10 percent variance             24.7           2 pca_Esd0U
#> 11 percent variance              8.91          3 pca_Esd0U
#> 12 percent variance              4.34          4 pca_Esd0U
#> 13 cumulative percent variance  62.0           1 pca_Esd0U
#> 14 cumulative percent variance  86.8           2 pca_Esd0U
#> 15 cumulative percent variance  95.7           3 pca_Esd0U
#> 16 cumulative percent variance 100             4 pca_Esd0U