PCA Signal Extraction

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

Usage

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.
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 variable names that will be populated elsewhere.
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 PC001 - 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, use either type = "coef" for the variable loadings per component or type = "variance" for how much variance each component accounts for.

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   
#> # … with 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_PMvd9
tidy(pca_estimates, number = 2)
#> # A tibble: 16 × 4
#>    terms      value component id       
#>    <chr>      <dbl> <chr>     <chr>    
#>  1 Murder   -0.536  PC1       pca_PMvd9
#>  2 Assault  -0.583  PC1       pca_PMvd9
#>  3 UrbanPop -0.278  PC1       pca_PMvd9
#>  4 Rape     -0.543  PC1       pca_PMvd9
#>  5 Murder    0.418  PC2       pca_PMvd9
#>  6 Assault   0.188  PC2       pca_PMvd9
#>  7 UrbanPop -0.873  PC2       pca_PMvd9
#>  8 Rape     -0.167  PC2       pca_PMvd9
#>  9 Murder   -0.341  PC3       pca_PMvd9
#> 10 Assault  -0.268  PC3       pca_PMvd9
#> 11 UrbanPop -0.378  PC3       pca_PMvd9
#> 12 Rape      0.818  PC3       pca_PMvd9
#> 13 Murder    0.649  PC4       pca_PMvd9
#> 14 Assault  -0.743  PC4       pca_PMvd9
#> 15 UrbanPop  0.134  PC4       pca_PMvd9
#> 16 Rape      0.0890 PC4       pca_PMvd9