Sparsify a Matrix via Column-wise Winner-Take-All

This function applies a "winner-take-all" sparsity model. For each column, it finds the single most significant entry based on specified sign constraints and sets all other entries in that column to zero.

sparsify_by_column_winner(
  X,
  first_column_constraint = c("none", "either", "positive", "negative"),
  default_constraint = c("either", "positive", "negative"),
  ensure_row_membership = TRUE
)

Arguments

X

A numeric matrix [p_features x k_components].

first_column_constraint

How to treat the first column. One of:

• `"none"`: (Default) The first column is left dense (not sparsified).

• `"either"`: The entry with the largest absolute value is kept, regardless of sign.

• `"positive"`: The largest entry with a positive sign is kept.

• `"negative"`: The entry with the largest magnitude (most negative) with a negative sign is kept.

default_constraint

How to treat all other columns (from the second onwards). Takes the same options as `first_column_constraint`. Defaults to `"either"`.

ensure_row_membership

Logical. If TRUE, ensures every feature is represented in at least one component by "reviving" the single most significant entry for any row that becomes all-zero after sparsity.

Value

A sparsified matrix with the same dimensions as X.

Details

It includes special handling for the first column, which often represents a main effect that may not require the same constraints as subsequent components.

Examples

set.seed(123)
mat <- matrix(c(
  -5, 0.1, 0.2, 0.3, 0.4,    # Col 1: Large negative value
   1, 2.0, 0.1, 0.2, 0.3,    # Col 2: Large positive value
  -1, -0.2, -3, -0.4, -0.5, # Col 3: Only negative values
  1, -2, 3, -4, 5           # Col 4: Mixed signs
), nrow = 5, ncol = 4)

res1 <- sparsify_by_column_winner(mat, 'positive', 'positive')