Analyze Harmonic Extensions for Local Extrema — analyze.harmonic.extensions • gflow

Complete workflow for analyzing how different harmonic extension methods perform on local extrema in a graph function. This function extracts subgraphs around each extremum and applies various harmonic extension methods for comparison.

Usage

analyze.harmonic.extensions(
  adj_list,
  weight_list,
  y,
  predictions,
  extrema_df,
  hop_offset = 2,
  min_hop_idx = 0,
  max_hop_idx = Inf,
  methods = c("weighted_mean", "harmonic_iterative", "harmonic_eigen",
    "biharmonic_harmonic", "boundary_smoothed"),
  max_iterations = 100,
  tolerance = 1e-06,
  sigma = 1,
  visualize = TRUE,
  save_results = FALSE,
  output_dir = "harmonic_extension_analysis",
  verbose = TRUE
)

Arguments

adj_list: Original graph adjacency list
weight_list: Original graph weight list
y: Original function values on vertices
predictions: Smoothed predictions (e.g., from spectral filtering)
extrema_df: Data frame containing extrema information
hop_offset: Additional hop distance beyond extremum's hop radius (default: 2)
min_hop_idx: Minimum hop index for extrema to process (default: 0)
max_hop_idx: Maximum hop index for extrema to process (default: Inf)
methods: Vector of harmonic extension methods to test
max_iterations: Maximum iterations for iterative methods (default: 100)
tolerance: Convergence tolerance (default: 1e-6)
sigma: Parameter for weighted mean method (default: 1.0)
visualize: Whether to visualize results (default: TRUE)
save_results: Whether to save detailed results (default: FALSE)
output_dir: Directory for saving results (default: "harmonic_extension_analysis")
verbose: Whether to print progress messages (default: TRUE)

Value

A list containing:

subgraphs: List of extracted subgraphs for each extremum
results: List of results from applying harmonic extension methods
metrics: Data frame with detailed metrics for all extrema and methods
summary: Data frame with summary statistics across methods
extrema_info: Data frame with information about processed extrema

Examples

if (FALSE) { # \dontrun{
result <- analyze.harmonic.extensions(
  graph$adj_list,
  graph$weight_list,
  y,
  gsf_res$predictions,
  gsf_b_cx$extrema_df,
  hop_offset = 2,
  min_hop_idx = 1,
  max_hop_idx = 5
)
} # }