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DataMembership: Gnostic Membership Test (Machine Gnostics)

The DataMembership class provides a robust method to test whether a value can be considered a member of a homogeneous data sample, using the EGDF (Estimating Global Distribution Function) framework. It determines the bounds within which new data points can be added to a sample without disrupting its homogeneity.

Overview

Membership Test: "Is a value Zξ a potential member of the given sample Z?" In other words: "Will the homogeneous sample Z remain homogeneous after extension by Zξ?"

Logic Process:

  1. Homogeneity Check: First, check if the sample Z is homogeneous using DataHomogeneity.
  2. Extension Test: If Z is homogeneous, extend the sample with a candidate value Zξ and check if the extended sample remains homogeneous.
  3. Bound Search: Determine the Lower Sample Bound (LSB) and Upper Sample Bound (USB).
    • LSB search range: [LB, DLB]
    • USB search range: [DUB, UB]
  4. Result: Find the minimum and maximum values of Zξ that preserve homogeneity.

Key Features

  • Homogeneity Preservation: Membership is defined by the preservation of sample homogeneity.
  • Adaptive Bound Search: Iteratively finds the exact boundaries where homogeneity is lost.
  • Diagnostic Visualization: Plots EGDF, PDF, and the determined membership bounds.

Parameters

Parameter Type Default Description
gdf EGDF - Fitted EGDF object (must be fitted and contain data).
verbose bool False If True, detailed logs are printed during execution.
catch bool True If True, errors and warnings are stored in params.
tolerance float 1e-3 Tolerance level for numerical calculations.
max_iterations int 100 Maximum number of iterations for bound search.
initial_step_factor float 0.001 Initial step size factor for adaptive bound search.

Attributes

  • LSB: float or None The calculated Lower Sample Bound.
  • USB: float or None The calculated Upper Sample Bound.
  • is_homogeneous: bool Indicates whether the original data sample is homogeneous.
  • params: dict Stores results, errors, warnings, and search parameters.
  • fitted: bool Indicates whether the membership analysis has been completed.

Methods

fit()

Performs the membership analysis to determine the Lower Sample Bound (LSB) and Upper Sample Bound (USB).

Returns: Tuple[Optional[float], Optional[float]] — The calculated LSB and USB values.

plot()

Generates a plot of the EGDF and PDF with membership bounds.

Parameters:

  • plot_smooth (bool, default=True): If True, plots smoothed curves.
  • plot (str, default='both'): 'gdf', 'pdf', or 'both'.
  • bounds (bool, default=True): If True, includes data bounds.
  • figsize (tuple, default=(12, 8)): Figure size.

Returns: None

results()

Returns the analysis results stored in the params attribute.

Returns: Dict[str, Any] — Analysis results including LSB, USB, homogeneity status, and parameters.

Example Usage

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

# 1. Prepare homogeneous data
data = np.array([ -13.5, 0, 1., 2., 3., 4., 5., 6., 7., 8., 9., 10.])

# 2. Fit EGDF
egdf = EGDF(data=data, catch=True)
egdf.fit()

# 3. Perform Membership Analysis
membership = DataMembership(gdf=egdf, verbose=True)
lsb, usb = membership.fit()

print(f"Lower Bound: {lsb}")
print(f"Upper Bound: {usb}")

# 4. Visualize Results
membership.plot()

# 5. Get detailed results
results = membership.results()
print(results)

Data Membership

Notes

  • Requirement: This analysis only works with EGDF objects.
  • Prerequisite: The initial sample must be homogeneous. If DataHomogeneity finds it non-homogeneous, the analysis proceeds no further.
  • Output: LSB and USB represent the safe range for extending the dataset while maintaining its structural distribution properties.

Author: Nirmal Parmar
Date: 2025-10-10