PCA Signal ExtractionSource:
step_pca creates a specification of a recipe step that will convert
numeric data into one or more principal components.
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.
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.
A logical to indicate if the quantities for preprocessing have been estimated.
The number of components to retain as new predictors. If
num_compis greater than the number of columns or the number of possible components, a smaller value will be used. If
num_comp = 0is set then no transformation is done and selected variables will stay unchanged.
A fraction of the total variance that should be covered by the components. For example,
threshold = .75means that
step_pcashould 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
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
xshould not be passed here (or at all).
A character string of variable names that will be populated elsewhere.
A character string for the prefix of the resulting new variables. See notes below.
A logical to keep the original variables in the output. Defaults to
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 = TRUEas it may affect the computations for subsequent operations.
A character string that is unique to this step to identify it.
An updated version of
recipe with the new step added to the
sequence of any existing operations.
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
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,
num_comp < 10, their names will be
num_comp = 101, the names would be
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.
tidy() this step, use either
type = "coef"
for the variable loadings per component or
type = "variance" for how
much variance each component accounts for.
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