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DataHomogeneity: Homogeneity Analysis for EGDF (Machine Gnostics)

The DataHomogeneity class provides robust, numerical homogeneity analysis for Estimating Global Distribution Functions (EGDF) by examining the shape and characteristics of their probability density functions (PDF). It is designed to detect outliers, clusters, and non-homogeneous structure in data using gnostic theory principles.

Overview

DataHomogeneity analyzes the fitted EGDF's PDF to determine if the underlying data is homogeneous. Homogeneity is defined by the presence of a single global maximum (unimodal PDF) and the absence of negative density values. The class uses robust peak detection, configurable smoothing, and comprehensive diagnostics to provide reliable results.

Gnostic vs. Statistical Homogeneity:
Gnostic homogeneity analysis is based on the algebraic and geometric properties of the data and the EGDF, not on statistical or probabilistic assumptions. It is deterministic, reproducible, and sensitive to both outliers and clusters, making it fundamentally different from classical statistical homogeneity tests.

  • Assumption-Free: No parametric or probabilistic assumptions.
  • Numerical: Decisions are made based on numerical analysis, not visual inspection.
  • Robust: Detects outliers and clusters via PDF maxima.
  • Diagnostic: Tracks errors, warnings, and analysis parameters.
  • Memory-Efficient: Optional flushing of large arrays after analysis.
  • Visualization: Built-in plotting for PDF and detected maxima.

Key Features

  • Automatic EGDF validation and homogeneity testing
  • Robust peak detection with configurable smoothing
  • Comprehensive error and warning tracking
  • Memory management with optional data flushing
  • Detailed visualization of analysis results
  • Integration with EGDF parameter systems

Parameters

Parameter Type Default Description
gdf EGDF required Fitted EGDF object (must have catch=True and be fitted)
verbose bool True Print detailed progress, warnings, and results
catch bool True Store all analysis results and metadata
flush bool False Clear large arrays after analysis to save memory
smoothing_sigma float 1.0 Gaussian smoothing parameter for PDF preprocessing
min_height_ratio float 0.01 Minimum relative height threshold for peak detection
min_distance int or None None Minimum separation between detected peaks (auto if None)

Attributes

  • is_homogeneous: bool or None
    Primary analysis result (None before fit, True/False after analysis)
  • picks: List[Dict]
    Detected maxima with detailed information (index, position, value, global flag)
  • z0: float or None
    Global optimum value from EGDF or detected from PDF
  • global_extremum_idx: int or None
    Array index of the global maximum
  • fitted: bool
    Indicates if analysis has been completed

Methods

fit(plot=False)

Performs comprehensive homogeneity analysis on the EGDF object.

  • plot: bool (optional)
    If True, generates plots for visual inspection of the analysis results

Returns:
bool — True if data is homogeneous, False otherwise

results()

Retrieves comprehensive homogeneity analysis results and metadata.

Returns:
dict — Contains keys such as 'is_homogeneous', 'picks', 'z0', 'global_extremum_idx', 'analysis_parameters', 'gdf_parameters', 'errors', 'warnings'

plot(figsize=(12, 8), title=None)

Visualizes the PDF, detected maxima, and homogeneity status.

  • figsize: tuple (default: (12, 8))
    Figure size in inches
  • title: str or None
    Custom plot title

Returns:
None (displays plot)

Example Usage

import numpy as np
from machinegnostics.magcal import EGDF, DataHomogeneity

# Homogeneous data
data = np.array([ -13.5, 0, 1., 2., 3., 4., 5., 6., 7., 8., 9., 10.])
egdf = EGDF(data=data, catch=True)
egdf.fit()

# Homogeneity analysis
homogeneity = DataHomogeneity(egdf, verbose=True)
is_homogeneous = homogeneity.fit(plot=True)
print(f"Data is homogeneous: {is_homogeneous}")

# Access results
results = homogeneity.results()
print(f"Number of maxima detected: {len(results['picks'])}")

Notes

  • Only supports EGDF objects (not QGDF, ELDF, or QLDF)
  • Homogeneity is defined by a single global maximum and no negative PDF values
  • Outliers and clusters are detected as additional maxima
  • Numerical analysis is preferred over visual inspection for reliability
  • Use flush=True for large datasets to save memory
  • All errors and warnings are tracked in the results dictionary

Author: Nirmal Parmar
Date: 2025-09-24