Soft DBSCAN-GM Documentation

🔍 Overview

Soft DBSCAN-GM is a fuzzy extension of the DBSCAN-GM algorithm. It combines density-based clustering with fuzzy logic by introducing membership degrees and iterative center updates using Mahalanobis distance.

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⚙️ Class Definition

Class Name: SoftDBSCANGM This class implements Soft DBSCAN-GM by first running DBSCAN and then refining membership degrees through fuzzy logic.

class SoftDBSCANGM:
    def __init__(self, eps: float = 0.5, min_samples: int = 5, m: float = 2.0,
                 max_iter: int = 100, tol: float = 1e-4):
        ...

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📋 Parameters

Parameter	Type	Default	Description
eps	float	0.5	DBSCAN epsilon radius for neighborhood detection
min_samples	int	5	Minimum number of points for DBSCAN core points
m	float	2.0	Fuzziness degree
max_iter	int	100	Maximum number of fuzzy iterations
tol	float	1e-4	Tolerance for convergence of cluster centers

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💻 Using Example

from soft_clustering._soft_dbscan_gm._soft_dbscan_gm import SoftDBSCANGM
from sklearn.datasets import make_moons
import numpy as np

X, _ = make_moons(n_samples=100, noise=0.1, random_state=42)

model = SoftDBSCANGM(eps=0.3, min_samples=5, m=2.0)
model.fit(X)

labels = model.predict()
membership = model.get_membership()

print("Labels:", labels)
print("Membership matrix:", membership)

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📥 Input / 📤 Output

• Input to fit(X):

  • X (np.ndarray): Input data (N x D)

• Returns:

  • Fuzzy membership matrix: get_membership() → array (N x K)

  • Hard labels: predict() → array (N,)

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🛠️ Methods

• fit(X): Fits the clustering model to the data

• get_membership(): Returns the fuzzy membership matrix

• predict(): Returns hard labels for each sample

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📝 Implementation Notes

• Initial clustering uses DBSCAN from scikit-learn

• Membership matrix initialized from DBSCAN labels

• Mahalanobis distance used in fuzzy updates

• Points marked as noise are treated as singleton clusters

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📚 Reference

1. Zhang, X., Xu, H., et al. (2016). Fuzzy density-based clustering method: Soft DBSCAN-GM.