Select Optimal r Using Multi-Criteria Approach for MPCA — select_r_multicriteria

Selects the optimal number of factors (r) for a given number of clusters (K) by combining multiple criteria: BIC, VAF, smoothness penalty, and VSS.

Usage

select_r_multicriteria_mpca(
  list_of_data,
  K,
  rvec = 1:6,
  vaf_threshold = 0.9,
  lambda_smooth = 0.001,
  vss_threshold = 0.5,
  weights = c(BIC = 1, VAF = 1, smoothness = 1, VSS = 1),
  max_iter = 50,
  nIterPCA = 5,
  tol = 0.001,
  method = "EM",
  n_init = 1,
  use_kmeans_init = TRUE,
  subject_rdim_for_kmeans = 2,
  mc_cores = 1,
  n_threads = 1
)

Arguments

list_of_data: A list of N matrices, each (T_i x M).
K: Number of clusters (fixed).
rvec: Vector of candidate r values to evaluate. Default is 1:6.
vaf_threshold: Minimum VAF threshold. Models with VAF below this are excluded. Default is 0.9.
lambda_smooth: Smoothness penalty weight. Default is 1e-3.
vss_threshold: Threshold for VSS criterion. Default is 0.5.
weights: Named vector of weights for each criterion. Default is c(BIC = 1, VAF = 1, smoothness = 1, VSS = 1).
max_iter: Maximum EM iterations.
nIterPCA: Sub-iterations for PCA update.
tol: Convergence tolerance.
method: "EM" or "closed_form".
n_init: Number of random initializations.
use_kmeans_init: Whether to use k-means initialization.
subject_rdim_for_kmeans: Dimension for k-means features.
mc_cores: Number of cores for parallelization.
n_threads: Number of OpenMP threads.

Value

A list with:

best_r: The selected r value.
summary: A data.frame with columns r, BIC, VAF, smoothness, VSS, composite_score.
best_model: The fitted model for the selected r.

Details

This function combines multiple criteria to select r:

BIC: Lower is better (penalizes complexity)
VAF: Higher is better (rewards fit quality)
Smoothness: Lower is better (penalizes wiggly factors)
VSS: Higher is better (rewards simple structure)

Each criterion is normalized to [0, 1] range, then combined using weights: $$ \text{score} = w_{\text{BIC}} \times \text{BIC}_{\text{norm}} + w_{\text{VAF}} \times (1 - \text{VAF}_{\text{norm}}) + w_{\text{smooth}} \times \text{smooth}_{\text{norm}} + w_{\text{VSS}} \times (1 - \text{VSS}_{\text{norm}}) $$

The r with the minimum composite score is selected among models satisfying VAF >= vaf_threshold.

Examples

if (FALSE) { # \dontrun{
result <- select_r_multicriteria_mpca(
  list_of_data, K = 3, rvec = 1:5,
  vaf_threshold = 0.9,
  lambda_smooth = 1e-3,
  weights = c(BIC = 1, VAF = 1, smoothness = 1, VSS = 1)
)
print(result$summary)
best_model <- result$best_model
} # }