sbm-k-too-small-arun.R

library(fastRG)
library(ggplot2)
library(vsp)

set.seed(29)

k <- 3
n <- 1000

B <- matrix(0.1, nrow = k, ncol = k)
diag(B) <- 0.8

sum(diag(B)) / (sum(B) - sum(diag(B)))

A <- dcsbm(
  theta = runif(n) + 1,
  k = k,
  B = B,
  expected_degree = 50
) |>
  sample_sparse()

fa_oracle <- vsp(A, rank = k, degree_normalize = FALSE)

plot_varimax_y_pairs(fa_oracle) +
  labs(
    title = "Optimal/lowest entropy rotation in correct dimension",
    subtitle = "Three block dc-sbm embedded into three dimensions"
  )

fa_k_low <- vsp(A, rank = 2, degree_normalize = FALSE)

plot_varimax_y_pairs(fa_k_low) +
  labs(
    title = "Points show up 'off axes' when embedding dimension is too low",
    subtitle = "Three block dc-sbm embedded into two dimensions"
  )