Cross validation on 2nd PC in sPCA

[cicadawing]

Apologies if this is a novice question!

I am also interested in CV for the PCs 2+. I was hoping, if you had time, to confirm that the below approach would be suitable? I was trying to follow some documentation with regards to the proposed iterative deflation method.

#Cross validation ACROSS PCs for regularisation values

regularisation_values <- seq(1, sqrt(ncol(X)), len=15)
SPC_Best_Reg <- list()
SPC_CV_Error <- list()
SPC_CV_Info <- list()

# Initialize the matrix for the first iteration
matrix_iter <- as.matrix(X)

wd <- ("XXX")
for (k in 1:25) {
  # Apply SPC.cv
  SPC_cv <- SPC.cv(matrix_iter, sumabsvs=regularisation_values, nfolds=10, trace=TRUE, center=TRUE, niter=10, orth=TRUE)
  SPC_Best_Reg[[k]] <- SPC_cv$bestsumabsv1se
  SPC_CV_Error[[k]] <- SPC_cv$cv.error
 
  #Save the info in a plot
  SPC_cv_plot <- ggplot() +
    geom_point(aes(x = regularisation_values, y = SPC_CV_Error[[k]]),
               color = "purple", shape = 16) +
    labs(x = "Regularisation Values", y = "Standard error of the average sum of squared error",
         title = paste0("CV Error vs Normalisation Values for PC", k)) +
    geom_vline(xintercept = SPC_Best_Reg[[k]], linetype = "dashed") +
    geom_text(aes(x = 12, y = max(SPC_CV_Error[[k]]) - 30000000),
              label = paste0("Best regularisation level: ", round(SPC_Best_Reg[[k]], 2)),
              hjust = 0, vjust = 0) +
    theme_minimal()
  print(SPC_cv_plot)
  # Add labeled repel
  if (capabilities(what = "png")) {
    CV_regularisations_doc <- body_add_gg(CV_regularisations_doc, value = SPC_cv_plot, style = "centered")
  }
 
  # Apply SPC without cv by adding 1 extra K
  SPC_applied <- SPC(matrix_iter, sumabsv=SPC_Best_Reg[[k]], K=1, center=TRUE, orth=TRUE, cnames=colnames(matrix_iter))
 
  # Store the result
  SPC_CV_Info[[k]] <- list()
  SPC_CV_Info[[k]][['u']] <- SPC_applied$u
  SPC_CV_Info[[k]][['d']] <- SPC_applied$d
  SPC_CV_Info[[k]][['v']] <- SPC_applied$v
  SPC_CV_Info[[k]][['prop_var_explained']] <- SPC_applied$prop.var.explained
 
  # Compute u, d, and transposed(v)
  # d is intended to be a diagonal matrix - so convert to diag
  # but ONLY if k > 1; diag() when k=1 results in issues
  transposed_v <- t(SPC_applied$v)
  udv <- SPC_applied$u %*% (SPC_applied$d) %*% transposed_v
 
  # Update the matrix for the next iteration
  matrix_iter <- as.matrix(matrix_iter - udv)
 
  print(CV_regularisations_doc, target = paste0(wd, "/SPC_cv_plot.docx"))
  saveRDS(SPC_Best_Reg, file =paste0(wd, "/SPC_GMV_Best_Reg.rds"))
  saveRDS(SPC_CV_Error, file =paste0(wd, "/SPC_GMV_CV_Error.rds"))
  saveRDS(SPC_CV_Info, file =paste0(wd, "/SPC_GMV_CV_Info.rds"))
}

Any guidance would be appreciated! Thanks for the great package!!!

Best wishes,