wjpy 0.1.0

Weighted Jaccard methodology for correlation network analysis. Bidirectional regime detection and pairing-family decomposition.

wjpy — Weighted Jaccard Methodology for Correlation Network Analysis

A Python package implementing the Weighted Jaccard (WJ) methodology and pairing-family decomposition for correlation network analysis. Detects bidirectional structural regimes — both convergence and divergence — and separates magnitude-component reorganization from sign-component reorganization.

Why WJ

Most correlation-network analysis collapses two structurally distinct reorganization modes into one number:

• Magnitude reorganization: correlations grow or shrink uniformly (financial crises).
• Sign reorganization: correlations flip polarity without changing magnitude (regime transitions, calm-era decorrelation).

wjpy implements the unsigned, signed, and binary Jaccard variants — and the gap between them — as separate, interpretable measurements. Validated empirically across genomics (GTEx v8 brain data), industrial sensors (NASA C-MAPSS, Scania, Tennessee Eastman), financial markets (S&P 500), and ecological systems.

Installation

pip install wjpy

Quick Start

import numpy as np
from wjpy import (
    fast_spearman_matrix,
    weighted_jaccard,
    signed_weighted_jaccard,
    binary_jaccard,
    implementation_divergence,
)

# Compute Spearman correlation matrix from observation data
# data shape: (n_features, n_samples)
data_baseline = np.random.randn(50, 200)
data_regime = np.random.randn(50, 200)

corr_baseline = fast_spearman_matrix(data_baseline)
corr_regime = fast_spearman_matrix(data_regime)

# Compare networks
wj_uns = weighted_jaccard(corr_baseline, corr_regime)
wj_sgn = signed_weighted_jaccard(corr_baseline, corr_regime)
bj = binary_jaccard(corr_baseline, corr_regime, threshold=0.3)

print(f"Unsigned WJ: {wj_uns:.4f}")
print(f"Signed WJ:   {wj_sgn:.4f}")
print(f"Binary J:    {bj:.4f}")

# Decompose reorganization into magnitude vs sign components
divergence = implementation_divergence(corr_baseline, corr_regime)
print(f"Sign inversion %: {divergence['sign_inversion_pct']:.1f}")
print(f"Magnitude %:      {divergence['magnitude_change_pct']:.1f}")

Functions

Function	Purpose
weighted_jaccard(corr_a, corr_b)	Unsigned WJ (magnitude reorganization)
signed_weighted_jaccard(corr_a, corr_b)	Signed WJ (magnitude + sign)
binary_jaccard(corr_a, corr_b, threshold)	Topological reorganization at edge threshold
implementation_divergence(corr_a, corr_b)	Decompose magnitude vs sign components
fast_spearman_matrix(data)	Vectorized Spearman correlation matrix
fast_pearson_matrix(data)	Vectorized Pearson correlation matrix
weighted_jaccard_chunked(vec_a, vec_b)	Memory-efficient WJ for >10M-element vectors

Methodology References

• Financial regime detection: Harbert, D.H. (2026). A Pairing-Family Decomposition of the Weighted Jaccard Index... Physica A (under review). Code: https://github.com/nwharbert8-ui/financial-wj-structural-regimes
• Genomics application: Harbert, D.H. (2026). Sigma-1 and Sigma-2 receptors exhibit divergent genome-wide co-expression architectures... Frontiers in Pharmacology, Neuropharmacology (in press).
• Industrial monitoring: Harbert, D.H. (2026). Weighted Jaccard decomposition detects sensor network reorganization preceding mechanical failure in turbofan engines, Scania trucks, and chemical processes. Mech. Syst. Signal Process. (under review).
• Ecological tipping points: Harbert, D.H. (2026). Weighted Jaccard similarity reveals water quality parameter reorganization preceding trophic state transitions. Ecological Indicators (under review).
• Pairing-family framework note: Layer 2H methodology, articulated 2026-04-29.

Premium Tier

The pairing-family decomposition implementations (Type 1 continuous-discrete, Type 2 sign-treatment, Type 5 local-global), full regime detection algorithms, macro-stress alignment utilities, and reference datasets per domain are available in a separate distribution wjpy-premium. Contact: [e-mail]

License

MIT License (core). See LICENSE.

Author

Drake H. Harbert Inner Architecture LLC, Canton, OH ORCID: 0009-0007-7740-3616 Email: [e-mail]

Citation

If you use wjpy in published work, please cite:

@software{harbert_wjpy_2026,
  author       = {Harbert, Drake H.},
  title        = {wjpy: Weighted Jaccard methodology for correlation network analysis},
  year         = 2026,
  publisher    = {Zenodo},
  doi          = {10.5281/zenodo.19025536},
  url          = {https://github.com/nwharbert8-ui/wjpy}
}