Backward greedy feature partition into two orderings (csmoothEM, warm-start only)

Warm-start backward greedy algorithm for partitioning features into two latent orderings. The procedure initializes ordering 1 once on all features, initializes ordering 2 once from a single seed feature via a rank-based 1D seed (no global ordering method), and then performs greedy moves using only warm-start updates (drop/append + a few EM iterations).

At each step, the algorithm selects the feature in ordering 1 with the largest positive gain \(\Delta_j = S_2(j \mid \Gamma_2) - S_1(j \mid \Gamma_1)\) and moves it to ordering 2, where \(S_k\) is computed by score_feature_given_Gamma under the current responsibilities.

This function never re-calls ordering initializers (e.g. fiedler/pcurve/PCA) after the initial construction. Ordering updates are done only via warm-start csmoothEM iterations.

backward_two_ordering_partition_csmooth(
  X,
  K = 50,
  init_method1 = c("fiedler", "PCA", "tSNE", "pcurve", "random"),
  seed2 = NULL,
  score_mode = c("ml", "none"),
  adaptive = NULL,
  rw_q = 2,
  relative_lambda = TRUE,
  lambda_min = 1e-10,
  lambda_max = 1e+10,
  discretization = c("quantile", "equal", "kmeans"),
  warm_iter_init = 10,
  warm_iter_refit = 5,
  max_steps = 50,
  verbose = TRUE,
  ...
)

Arguments

X

Numeric matrix (n x d).

K

Integer \(\ge 2\). Number of mixture components.

init_method1

Ordering initializer for ordering 1, passed to initialize_csmoothEM.

seed2

Optional integer. If NULL, chosen as the worst-aligned feature under ordering 1.

score_mode

One of "ml" or "none"; passed to score_feature_given_Gamma.

adaptive

Adaptive mode used in do_csmoothEM warm updates ("ml" or "none"). If NULL, defaults to score_mode.

rw_q

Integer \(\ge 0\). RW rank deficiency.

relative_lambda

Logical.

lambda_min, lambda_max

Bounds for lambda optimization when score_mode="ml".

discretization

Discretization used in initialization (recommended: "quantile").

warm_iter_init

Initial warm-start iterations for ordering 1.

warm_iter_refit

Warm-start iterations after each move (applied to both fits).

max_steps

Maximum number of greedy moves.

verbose

Logical.

...

Passed to initialize_csmoothEM for ordering 1.

Value

A list with:

  • assign: character vector length d in c("A","B").

  • J1, J2: feature indices (original X column indices) in each ordering.

  • seedB: seed feature index for ordering 2.

  • fit1, fit2: csmooth_em objects for each ordering.

  • history: data.frame of moves (feature, gain, sizes).