fn-dbscan 0.1.0

Fuzzy Neighborhood DBSCAN clustering algorithm

FN-DBSCAN: Fuzzy Neighborhood DBSCAN

Implementation of Fuzzy Neighborhood DBSCAN (FN-DBSCAN), a density-based clustering algorithm that extends classic DBSCAN using fuzzy theory.

Installation

git clone https://github.com/onurceldir123/fn-dbscan.git
cd fn-dbscan
pip install -e .

Requirements: Python ≥3.8, NumPy, scikit-learn, scipy

Quick Start

from sklearn.datasets import make_moons
from fn_dbscan import FN_DBSCAN

X, _ = make_moons(n_samples=200, noise=0.05, random_state=42)

model = FN_DBSCAN(
    eps=0.1,                  
    min_fuzzy_neighbors=5.0,    
    min_membership=0.0,        
    fuzzy_function='exponential', 
    normalize=True              
)

labels = model.fit_predict(X)

print(f"Found {model.n_clusters_} clusters")

Why FN-DBSCAN?

While classic DBSCAN is powerful, it relies on a "crisp" boundary—a point is either a neighbor or it isn't. FN-DBSCAN improves upon this by introducing fuzzy set theory:

• [cite_start]Robustness to Density Variations: It is more robust than DBSCAN when handling datasets with varying densities and shapes[cite: 19, 61].
• Soft Boundaries: Instead of an all-or-nothing approach, it calculates a "fuzzy cardinality" (sum of membership degrees). [cite_start]This handles border points and noise more naturally [cite: 153-155].
• [cite_start]Scale Invariance: The implementation includes the normalization technique proposed in the paper, making the eps parameter adaptable to the data scale [cite: 127-141].
• [cite_start]Best of Both Worlds: Combines the speed of DBSCAN with the robustness of fuzzy clustering methods like NRFJP[cite: 18, 60].

Parameters

Core Parameters

Parameter	Type	Default	Description
eps	float	0.5	Maximum neighborhood radius (0-1 for normalized data).
min_fuzzy_neighbors	float	5.0	Minimum fuzzy cardinality to be a core point (analogous to min_samples in DBSCAN).
min_membership	float	0.0	Minimum membership threshold ($\epsilon_1$). Points with membership below this are ignored.
fuzzy_function	str	'linear'	Membership function: 'linear', 'exponential', or 'trapezoidal'.
normalize	bool	True	Normalize data to make eps scale-independent (Strongly Recommended).
k	float	None	Steepness parameter. Controls how fast membership drops. Higher $k$ = stricter neighborhood. Auto-calculated as $d_{max}/\epsilon$ if None.
metric	str	'euclidean'	Distance metric (any scikit-learn compatible metric).

Fuzzy Functions

• 'exponential' - Recommended for most cases, especially non-convex clusters
• 'linear' - Simple linear decay, good for well-separated clusters
• 'trapezoidal' - Maintains full membership for very close points

Model Attributes

After fitting, the model provides:

• labels_ - Cluster labels for each sample (-1 for noise)
• core_sample_indices_ - Indices of core points
• n_clusters_ - Number of clusters found

Algorithm Overview

FN-DBSCAN extends DBSCAN by computing fuzzy cardinality instead of discrete point counts:

Traditional DBSCAN:  cardinality = count(neighbors)
FN-DBSCAN:          cardinality = Σ membership(distance(p, q))

A point is a core point if its fuzzy cardinality ≥ min_fuzzy_neighbors.

Citation

If you use FN-DBSCAN in your research, please cite the original paper:

@article{nasibov2009robustness,
  title={Robustness of density-based clustering methods with various neighborhood relations},
  author={Nasibov, Efendi N and Ulutagay, G{\"o}zde},
  journal={Fuzzy Sets and Systems},
  volume={160},
  number={24},
  pages={3601--3615},
  year={2009},
  publisher={Elsevier}
}

License

MIT License - see LICENSE file for details.

Contributing

Contributions welcome! Please open an issue or submit a pull request on GitHub.

---

Reference: Nasibov, E. N., & Ulutagay, G. (2009). Robustness of density-based clustering methods with various neighborhood relations. Fuzzy Sets and Systems, 160(24), 3601-3615.