Exact search for a partial principal balance on grouped parts

Finds the grouped balance with maximum variance among all assignments whose number of active groups is between min_parts and max_parts.

partial_pb_exact(
  X,
  lI = NULL,
  min_parts = 2,
  max_parts = NULL,
  method = "restricted"
)

Arguments

X: A numeric matrix with strictly positive finite entries. Rows are observations and columns are compositional parts.
lI: A list defining a partition of a subset of the columns of X. If NULL, each column of X is used as a singleton group.
min_parts: Integer. Minimum number of active groups.
max_parts: Integer or NULL. Maximum number of active groups. If NULL, all groups may be active.
method: Exhaustive search method. Currently only "restricted" is implemented; it enumerates only supports whose sizes are inside the requested range and assigns signs in binary Gray-code order.

Value

A list with the following elements:

dim: Dimension of the grouped problem, equal to length(lI) - 1.
lI: The input grouping structure.
variance: Variance criterion of the best grouped balance.
balance_raw: Integer vector in \(\{-1,0,1\}\) describing the best grouped split.
balance: The corresponding one-column balance basis.
min_parts: Minimum number of active groups.
max_parts: Maximum number of active groups.

Details

The search enumerates only supports whose size is between min_parts and max_parts. For each support, signs are generated in binary Gray-code order, fixing the first active group on the left side to avoid evaluating both a balance and its sign reversal.