Bipartite (Rectangular) DC-LBM Backend for MONECA Segmentation

Rectangular counterpart of [moneca_sbm()]. Accepts a two-mode mobility matrix (rows and columns are distinct entity types, e.g. persons x employers, workers x occupations) and fits a hierarchical degree-corrected Latent Block Model (`greed::DcLbm`). The rectangular relative-risk matrix `RR = O / E` acts as the DcLbm residual under identity block interaction, mirroring the square RR = DC-SBM bridge that underpins `moneca_sbm()`.

Usage

moneca_bipartite(
  mx,
  backend = "greed",
  deg_corr = TRUE,
  edge_model = "poisson",
  small.cell.reduction = 0,
  margin_policy = c("row_col", "none"),
  segment.levels = NULL,
  auto_method = c("mdl", "mi_plateau"),
  max_K = NULL,
  seed = NULL,
  n_init = 1L,
  has_margins = "auto",
  verbose = FALSE,
  ...
)

Arguments

mx: A rectangular mobility matrix of shape `n_row x n_col`. Optional moneca-style margins in the last row and column are auto-detected when `has_margins = "auto"`. Sparse `dgCMatrix` input is supported end to end.
backend: Currently only `"greed"` (DcLbm via the `greed` package). Argument kept for forward compatibility with future bipartite backends.
deg_corr: Logical. Reserved. `greed::DcLbm` is always degree corrected; a non-default value is silently accepted but has no effect.
edge_model: One of `"poisson"` (default, appropriate for count-valued mobility) or `"bernoulli"`. Reserved. DcLbm uses the Poisson edge model; non-default values emit a warning and are otherwise ignored.
small.cell.reduction: Numeric. Cells in the core rectangle with values below this threshold are zeroed before RR computation. Mirrors the `moneca::moneca_fast()` parameter.
margin_policy: One of `"row_col"` (default; append margins to each one-mode projection, matching moneca's convention) or `"none"` (skip appending margins). `"row_col"` is the load-bearing choice for downstream moneca compatibility.
segment.levels: Integer, `NULL`, or the string `"auto"`. If `NULL` (default), all hierarchy levels produced by the backend (from the finest joint `K` down to `2`) are returned. If an integer, the hierarchy is truncated to that many approximately log-spaced levels. If `"auto"`, the full hierarchy is fit and then [auto_segment_levels()] picks a preferred level **independently per side**; `$rows` and `$cols` are trimmed accordingly and each carries the picker result under `$auto_level`. The two sides may end up at different levels.
auto_method: One of `"mdl"` (default) or `"mi_plateau"`. Ignored unless `segment.levels = "auto"`.
max_K: Integer or `NULL`. Reserved for backend-specific caps; the `greed` backend currently uses its internal default.
seed: Integer seed for reproducible inference.
n_init: Integer. Number of independent backend runs; the best-scoring fit (highest ICL) is retained. Defaults to `1L`.
has_margins: One of `"auto"` (default), `TRUE`, or `FALSE`. Controls whether to detect and/or append row/column margins to the input matrix.
verbose: Logical. If `TRUE`, prints backend progress.
...: Additional arguments forwarded to the backend.

Value

An object of class `"moneca_bipartite"` with slots: * `rows` - full moneca-class object for the row view (one-mode projection on rows). * `cols` - full moneca-class object for the column view. * `bipartite_diagnostics` - list with backend metadata, per-level row / column block counts, joint ICL / MDL traces, and per-level `Krow x Kcol` block-interaction matrices computed directly from the rectangular core.

Details

Because `moneca::weight.matrix()` and the downstream `segment.*()` stack assume square inputs, the bipartite fit is exposed to moneca through two linked moneca-class objects built from one-mode projections of the rectangular RR. The row view uses `RR column view the transpose, with `D_c = diag(col_margin / grand_total)` (analogously for rows). Each projection is zero-diagonal, symmetric, sparse, and carries moneca-style margins appended as the last row and column.

The row view and column view each expose the full moneca output contract (`segment.list`, `mat.list`, `segment_metadata`, and companion scalars). `moneca::segment.membership()`, `moneca::segment.quality()`, `moneca::plot_moneca_ggraph()`, and `moneca::plot_moneca_hierarchical()` run unchanged on `out$rows` or `out$cols`.

The joint `Krow x Kcol` co-clustering is not representable as a single square moneca object. It is preserved in `bipartite_diagnostics$block_interaction_matrix_per_level`, which cross-tabulates the rectangular core by row and column memberships at each level.

Examples