Package 'Entropic.Scree'

Entropic Scree Dimensionality Estimation (v1.0.1)

Description

An information-theoretic diagnostic technique for estimating the intrinsic dimensionality of tabular datasets. Evaluates shared probability mass via a transformed mutual information metric. Aims to extract the Intrinsic Generative Rank (r) and structural topology. For full methodological details, see the preprint at https://zenodo.org/records/22028087.

Usage

Entropic.Scree(
  data,
  low_entropy_thresh = 0.05,
  num_bins = NULL,
  bin_multiplier = 1,
  num_cores = parallel::detectCores() - 2,
  interactive_mode = TRUE,
  purge_constants = TRUE,
  check_collinearity = TRUE,
  triple_tap_window = 20,
  fwer_alpha = 0.01,
  extract_eigenvectors = FALSE,
  extract_bipolar_modules = FALSE,
  bipolar_top_n = 0.2,
  return_processed_data = FALSE
)

Arguments

data	A data.table containing the dataset to evaluate. Base data.frames are not supported.
low_entropy_thresh	Numeric. Minimum marginal entropy threshold. Default is 0.05.
num_bins	Integer. Number of bins for discretization. Default is NULL (auto-calculated).
bin_multiplier	Numeric. Multiplier for the automatic bin calculation. Default is 1.0.
num_cores	Integer. Number of CPU cores for OpenMP parallelization.
interactive_mode	Logical. If TRUE, displays plot and prompts user to confirm ranks.
purge_constants	Logical. If TRUE, automatically removes zero-variance variables.
check_collinearity	Logical. If TRUE, purges perfectly collinear variables.
triple_tap_window	Integer. Window size for the triple-tap heuristic. Default is 20.
fwer_alpha	Numeric. Family-wise error rate alpha threshold. Default is 0.01.
extract_eigenvectors	Logical. If TRUE, extracts and returns eigenvectors.
extract_bipolar_modules	Logical. If TRUE, forces eigenvector extraction to build topological poles.
bipolar_top_n	Numeric. Proportion of top variables to include in poles.
return_processed_data	Logical. If TRUE, includes the processed data.table in the output.

Value

A list of class "entropic_scree" containing the following components:

eigenvalues	A numeric vector of extracted eigenvalues.
similarity_matrix	The double-centered mutual information matrix.
retained_features	A character vector of variables that passed entropy thresholds.
bin_distributions	A table of bin counts for the discretized data.
R_eff	Total Unique Probabilistic Volume scalar.
K_log_gap	Integer estimate for the Observed Generative Rank.
K_triple_tap	Integer estimate for the Extended Signal Tail.
triple_tap_multiplier	The local dynamic t-multiplier used in Engine B.
K_roots	The finalized integer representing the Intrinsic Generative Rank.
K_extended	The finalized integer representing the Extended Signal Tail.
top_of_bulk	Index marking the boundary of idiosyncratic variance.
total_signal_volume	Total shared signal volume scalar.
unique_signal_volume	Unique signal volume scalar.
redundant_signal_volume	Redundant signal volume scalar.
idiosyncratic_volume	Idiosyncratic informational variance scalar.
AIG	Average Informational Gravity variable equivalent.
FSIG_final	A numeric vector of Factor-Specific Informational Gravity.
structural_topology_profile	A numeric vector of relative factor gravities.
FSIG_extended_bulk	Extended FSIG metric utilizing the macro bulk bound.
FSIG_extended_kaiser	Extended FSIG metric utilizing the Kaiser bound.
eigenvectors	A matrix of extracted eigenvectors, if requested.
bipolar_modules	A structured list of topological extraction poles, if requested.
processed_data	The pre-processed data.table, if requested.

Examples

# Generate a small random dataset
dummy_data <- data.table::data.table(
  V1 = rnorm(50),
  V2 = rnorm(50),
  V3 = rnorm(50)
)

# Run the estimation (interactive_mode MUST be FALSE for automated checks)
res <- Entropic.Scree(dummy_data, interactive_mode = FALSE, num_cores = 1)

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Update Entropic Scree Rank Estimates

Description

A companion function to modify the rank estimates of a previously evaluated Entropic Scree object. This allows users to recalculate informational gravity and structural composition without re-running the computationally expensive C++ mutual information engine.

Usage

Update.Entropic.Scree(
  scree_obj,
  new_K_roots = NULL,
  new_K_extended = NULL,
  bipolar_top_n = 0.2,
  interactive_mode = TRUE
)

Arguments

scree_obj	A valid output list from Entropic.Scree().
new_K_roots	Integer. The new Observed Generative Rank. If NULL, retains original.
new_K_extended	Integer. The new Extended Signal Tail Rank. If NULL, retains original.
bipolar_top_n	Numeric. Proportion of top variables to include in newly extracted poles.
interactive_mode	Logical. If TRUE, prints updated metric dashboards to the console.

Value

A mutated list of class "entropic_scree" containing the updated structural topology profiles, signal volumes, and informational gravity metrics based on the new rank thresholds.

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