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

step_ica(
recipe,
...,
role = "predictor",
trained = FALSE,
num_comp = 5,
options = list(method = "C"),
res = NULL,
prefix = "IC",
keep_original_cols = FALSE,
skip = FALSE,
id = rand_id("ica")
)

## 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. 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 ICA 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. A list of options to fastICA::fastICA(). No defaults are set here. Note that the arguments X and n.comp should not be passed here. The fastICA::fastICA() object is stored here once this preprocessing step has be trained by prep.recipe(). 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 FALSE. 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. 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

Independent component analysis (ICA) is a transformation of a group of variables that produces a new set of artificial features or components. ICA assumes that the variables are mixtures of a set of distinct, non-Gaussian signals and attempts to transform the data to isolate these signals. Like PCA, 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. Also like PCA, it is advisable to center and scale the variables prior to running ICA.

This package produces components using the "FastICA" methodology (see reference below). This step requires the dimRed and fastICA packages. If not installed, the step will stop with a note about installing these packages.

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 IC1 - IC9. If num_comp = 101, the names would be IC001 - IC101.

When you tidy() this step, a tibble with columns terms (the selectors or variables selected), value (the loading), and component is returned.

## References

Hyvarinen, A., and Oja, E. (2000). Independent component analysis: algorithms and applications. Neural Networks, 13(4-5), 411-430.

Other multivariate transformation steps: step_classdist(), step_depth(), step_geodist(), step_isomap(), step_kpca_poly(), step_kpca_rbf(), step_kpca(), step_mutate_at(), step_nnmf(), step_pca(), step_pls(), step_ratio(), step_spatialsign()

## Examples

# from fastICA::fastICA
set.seed(131)
S <- matrix(runif(400), 200, 2)
A <- matrix(c(1, 1, -1, 3), 2, 2, byrow = TRUE)
X <- as.data.frame(S %*% A)

tr <- X[1:100, ]
te <- X[101:200, ]

rec <- recipe( ~ ., data = tr)

ica_trans <- step_center(rec,  V1, V2)
ica_trans <- step_scale(ica_trans, V1, V2)
ica_trans <- step_ica(ica_trans, V1, V2, num_comp = 2)

if (require(dimRed) & require(fastICA)) {
ica_estimates <- prep(ica_trans, training = tr)
ica_data <- bake(ica_estimates, te)

plot(te$V1, te$V2)
plot(ica_data$IC1, ica_data$IC2)

tidy(ica_trans, number = 3)
tidy(ica_estimates, number = 3)
}
#>
#> Attaching package: ‘kernlab’
#> The following object is masked from ‘package:ggplot2’:
#>
#>     alpha
#>
#> Attaching package: ‘dimRed’
#> The following object is masked from ‘package:stats’:
#>
#>     embed
#> The following object is masked from ‘package:base’:
#>
#>     as.data.frame

#> # A tibble: 4 × 4
#>   terms component  value id
#>   <chr> <chr>      <dbl> <chr>
#> 1 V1    IC1       -1.04  ica_3zAWC
#> 2 V1    IC2       -0.378 ica_3zAWC
#> 3 V2    IC1       -0.773 ica_3zAWC
#> 4 V2    IC2        0.788 ica_3zAWC