Select an Optimal Joint Number of Components for Multi-View Data

This function determines a single optimal number of components (k) to represent a multi-view dataset by analyzing the joint variance explained curve. It offers multiple methods for selecting k and includes a built-in self-test to verify its own correctness.

select_joint_k(
  mat_list = NULL,
  method = c("pca", "spca"),
  k_max = NULL,
  sparsity = 0.5,
  selection_method = c("elbow", "threshold"),
  variance_threshold = 0.9,
  self_test = FALSE
)

Arguments

mat_list: A list of numeric matrices [subjects x features]. Required unless `self_test = TRUE`.
method: The decomposition method. One of `"pca"` (fast SVD-based) or `"spca"`.
k_max: The maximum number of components to consider.
sparsity: A single sparsity parameter (0-1) for SPCA. Ignored for PCA.
selection_method: The method for choosing k. One of `"elbow"` (point of maximum deviation from a straight line of improvement) or `"threshold"`.
variance_threshold: The proportion of variance (0-1) to be explained. Only used when `selection_method = "threshold"`.
self_test: Logical. If TRUE, the function will ignore all other inputs, run a built-in suite of tests on simulated data, and print the results. This is for verifying the function's integrity. Defaults to FALSE.

Value

If `self_test = FALSE`, a list containing:

`optimal_k`: The selected optimal number of components.
`joint_variance_curve`: A tibble with `k` and the cumulative proportion of variance explained at each `k`.
`plot`: A ggplot object visualizing the results.

If `self_test = TRUE`, it prints test results and returns invisibly.