`step_pca()`

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

## 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`

.

## See also

Other multivariate transformation steps:
`step_classdist_shrunken()`

,
`step_classdist()`

,
`step_depth()`

,
`step_geodist()`

,
`step_ica()`

,
`step_isomap()`

,
`step_kpca_poly()`

,
`step_kpca_rbf()`

,
`step_kpca()`

,
`step_mutate_at()`

,
`step_nnmf_sparse()`

,
`step_nnmf()`

,
`step_pls()`

,
`step_ratio()`

,
`step_spatialsign()`

## 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
```