Composing Projectors: Chaining Models • multivarious

compose_partial_projector() chains fitted projector objects whose dimensions line up. The output scores from one stage become the input data for the next stage, and the composed object can then be used with the same core verbs as a single projector: project(), partial_project(), coef(), inverse_projection(), and reconstruct().

Composition is for fitted projectors, not for standalone preprocessing steps. Use a model’s preproc argument for centering, scaling, or other preprocessing that should happen inside a stage. Use composition when one fitted projection is itself the training data for a later fitted projection.

1. Fit compatible stages

This example fits a PCA on the original variables, then fits a second PCA on the scores from the first PCA. The first stage maps 15 variables to 8 scores. The second stage maps those 8 scores to 7 final scores.

set.seed(1)

X <- matrix(rnorm(30 * 15), nrow = 30, ncol = 15)

p1 <- pca(X, ncomp = 8)
p2 <- pca(scores(p1), ncomp = 7)

pipe <- compose_partial_projector(
  first = p1,
  second = p2
)

summary(pipe)
#> # A tibble: 2 × 5
#>   stage name   in_dim out_dim class
#>   <int> <chr>   <int>   <int> <chr>
#> 1     1 first      15       8 pca  
#> 2     2 second      8       7 pca

The summary is the first check to make: adjacent stages must have matching output and input dimensions.

2. Project through the whole chain

Projecting with the composed object is equivalent to applying each stage in sequence.

scores_pipe <- project(pipe, X)
dim(scores_pipe)
#> [1] 30  7

The infix operator %>>% is a shorter spelling for the same composition.

pipe_with_operator <- p1 %>>% p2
dim(project(pipe_with_operator, X))
#> [1] 30  7

3. Use a subset of original variables

partial_project() on a composed projector supports partial projection at the first stage. The colind vector names the original columns supplied to that first stage; all later stages receive the full output from the preceding stage.

cols <- 1:5
scores_subset <- partial_project(
  pipe,
  X[, cols, drop = FALSE],
  colind = cols
)

dim(scores_subset)
#> [1] 30  7

Later-stage column subsetting is not currently implemented for composed projectors. Supplying a list with non-NULL entries after the first stage emits a warning and those later entries are ignored.

4. Inspect the combined linear map

For linear projectors such as PCA, coef() returns the effective coefficient matrix for the whole chain: original variables by final components.

V <- coef(pipe)
dim(V)
#> [1] 15  7

variables_used() and vars_for_component() inspect this combined coefficient matrix. With dense PCA stages, every original variable usually contributes to the final scores.

c(
  variables_used = length(variables_used(pipe)),
  variables_for_first_component = length(vars_for_component(pipe, 1))
)
#>                variables_used variables_for_first_component 
#>                            15                            15

5. Reconstruct from final scores

reconstruct() maps final scores back toward the original variable space using the inverse projection for each stage. Because both PCA stages reduce dimension, the reconstruction is a lossy approximation, not an exact inverse.

X_hat <- reconstruct(pipe, scores_pipe)

c(
  rows = nrow(X_hat),
  columns = ncol(X_hat),
  rmse = sqrt(mean((X - X_hat)^2))
)
#>       rows    columns       rmse 
#> 30.0000000 15.0000000  0.4487182

6. Truncate the final stage

truncate() reduces the number of components retained from the last stage of a composed projector. It does not refit or truncate intermediate stages.

pipe4 <- truncate(pipe, ncomp = 4)

summary(pipe4)
#> # A tibble: 2 × 5
#>   stage name   in_dim out_dim class
#>   <int> <chr>   <int>   <int> <chr>
#> 1     1 first      15       8 pca  
#> 2     2 second      8       4 pca
dim(project(pipe4, X))
#> [1] 30  4

7. Practical boundaries

Composition is useful when the stages form a valid sequence of fitted projectors. The output dimension of each stage must match the input dimension of the next stage. For preprocessing, use each model’s preprocessing argument. For partial projection, treat colind as a first-stage feature subset; it does not target later stages.