PCA Signal Extraction

Source: R/pca.R

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

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

# S3 method for step_pca
tidy(x, type = "coef", ...)

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_comp

The number of PCA 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.
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\ Note: using this argument will override and resent 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.recipe().
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
id

A character string that is unique to this step to identify it.
x

A step_pca object.
type

For the tidy() method, either "coef" (for the variable loadings per component) or "variance" (how much variance does each component account for).

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), value (the loading), and component.

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.

References

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

See also

step_ica() step_kpca() step_isomap() recipe() prep.recipe() bake.recipe()

Examples

rec <- recipe( ~ ., data = USArrests)
pca_trans <- rec %>%
  step_center(all_numeric()) %>%
  step_scale(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_center(all_numeric()) %>%
  step_scale(all_numeric()) %>%
  step_pca(all_numeric(), threshold = .99)
with_thresh <- prep(with_thresh, training = USArrests)
bake(with_thresh, USArrests)

#> # A tibble: 50 x 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 = 3)

#> # A tibble: 1 x 4
#>   terms         value component id       
#>   <chr>         <dbl> <chr>     <chr>    
#> 1 all_numeric()    NA NA        pca_YT48I
tidy(pca_estimates, number = 3)

#> # A tibble: 16 x 4
#>    terms      value component id       
#>    <chr>      <dbl> <chr>     <chr>    
#>  1 Murder   -0.536  PC1       pca_YT48I
#>  2 Assault  -0.583  PC1       pca_YT48I
#>  3 UrbanPop -0.278  PC1       pca_YT48I
#>  4 Rape     -0.543  PC1       pca_YT48I
#>  5 Murder    0.418  PC2       pca_YT48I
#>  6 Assault   0.188  PC2       pca_YT48I
#>  7 UrbanPop -0.873  PC2       pca_YT48I
#>  8 Rape     -0.167  PC2       pca_YT48I
#>  9 Murder   -0.341  PC3       pca_YT48I
#> 10 Assault  -0.268  PC3       pca_YT48I
#> 11 UrbanPop -0.378  PC3       pca_YT48I
#> 12 Rape      0.818  PC3       pca_YT48I
#> 13 Murder    0.649  PC4       pca_YT48I
#> 14 Assault  -0.743  PC4       pca_YT48I
#> 15 UrbanPop  0.134  PC4       pca_YT48I
#> 16 Rape      0.0890 PC4       pca_YT48I