Compute Gradient Flow Modulation Weights

Computes modulation factors for gradient flow based on vertex density and/or edge length distribution. Returns modulated edge weights along with intermediate objects for inspection and debugging.

Usage

compute.gfc.modulation(
  adj.list,
  weight.list,
  modulation = c("density", "edgelen", "density_edgelen"),
  density = NULL,
  edgelen.bandwidth = "auto",
  normalize.weights = TRUE,
  verbose = TRUE
)

Arguments

adj.list: Graph adjacency list (1-based indexing).
weight.list: Edge weight list (edge lengths).
modulation: Character string specifying modulation type. "density" for vertex density modulation (edges weighted by target vertex density), "edgelen" for edge length modulation (edges weighted by length distribution density), or "density_edgelen" for combined modulation (product of both).
density: Optional numeric vector of pre-computed density values. If NULL, computed from nearest neighbor distances (raw d1 inverse). Smoothed density must be estimated externally; the archived rdgraph-based helper is gflowx::compute.smoothed.density().
edgelen.bandwidth: Bandwidth for edge length KDE. If "auto" (default), uses Sheather-Jones method via bw.SJ(). Can also be a positive numeric value for manual bandwidth, or a character string for other bandwidth selectors: "nrd0", "nrd", "ucv", "bcv", or "SJ".
normalize.weights: Logical; if TRUE (default), normalize modulated weights so that for each vertex the maximum outgoing weight equals the original maximum.
verbose: Logical; print progress information.

Value

An object of class "gfc_modulation" containing:

modulated.weight.list: List of modulated edge weights.
modulation: The modulation type used.
density: Vertex density values (NULL if not computed).
density.raw: Logical; TRUE if density was computed internally (raw d1 inverse).
edgelen.weights: Named list of edge length weights, where names are "v-u" for edge from v to u (NULL if not computed).
edgelen.bandwidth: Bandwidth used for edge length KDE.
edgelen.kde: The full density object from R's density() function, useful for plotting and inspection.
edgelen.lengths: Vector of all unique edge lengths.
edgelen.densities: KDE density at each edge length (before normalization).
n.vertices: Number of vertices.
n.edges: Number of unique edges.

Details

The modulation factors are applied to edge weights as follows. For an edge from v to u with original weight w(v,u), the modulated weight is: for "density", w'(v,u) = w(v,u) * rho(u); for "edgelen", w'(v,u) = w(v,u) * dl(v,u); for "density_edgelen", w'(v,u) = w(v,u) * rho(u) * dl(v,u). Here rho(u) is the density at vertex u and dl(v,u) is the edge length density weight.

Usage

Arguments

Value

Details

See also