Possibilistic Fuzzy C-Means (PFCM)

A robust soft clustering algorithm combining fuzzy memberships and outlier-aware typicalities.

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🔍 Overview

The Possibilistic Fuzzy C-Means (PFCM) algorithm clusters data by assigning both:

• Fuzzy memberships to model soft belonging across multiple clusters

• Possibilistic typicalities to identify and suppress noisy or atypical points

This dual mechanism improves on standard FCM by being more robust to noise and avoiding cluster collapse, making it ideal for ambiguous data and real-world use.

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⚙️ Class Definition

class soft_clustering.PFCM(
    n_clusters: int,
    m: float = 2.0,
    eta: float = 2.0,
    a: float = 1.0,
    b: float = 1.0,
    max_iter: int = 150,
    tol: float = 1e-5,
    random_state: Optional[int] = None
)

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📋 Parameters

Parameter	Type	Default	Description
n_clusters	int	—	Number of clusters to form.
m	float	2.0	Fuzzifier for membership values.
eta	float	2.0	Fuzzifier for typicality values.
a	float	1.0	Weight for membership influence in centroid update.
b	float	1.0	Weight for typicality influence in centroid update.
max_iter	int	150	Maximum number of iterations.
tol	float	1e-5	Tolerance for convergence.
random_state	Optional[int]	None	Seed for reproducible centroid initialization.

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🚀 Usage Example

from soft_clustering import PFCM

# Create a simple dataset
data = [[1.0, 1.1], [0.9, 0.95], [5.1, 5.2], [5.0, 5.1], [9.0, 1.0]]

# Initialize and train the model
model = PFCM(n_clusters=3, random_state=0)
model.fit(data)

# Access results
print("Cluster centers:", model.cluster_centroids)
print("Memberships:", model.membership_matrix)
print("Typicalities:", model.typicality_matrix)

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🛠️ Methods

fit(X)

Train the model on input data.

Parameters:

• X (Union[np.ndarray, List[List[float]]]): Data matrix with shape (n_samples, n_features).

Returns:

• self: Trained model instance.

predict_typicalities(X)

Compute typicalities for new data points.

Returns:

• membership_matrix (np.ndarray, shape (s,n_samples)): Membership Matrix.

predict_typicalities(X)

Compute typicalities for new data points.

Returns:

• typicality_matrix (np.ndarray, shape (c, n_samples)): Typicality matrix.

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📝 Notes

• Suitable for small and medium datasets.

• Typicalities highlight noise and are useful for filtering outliers.

• Combines the best of fuzzy logic and possibilistic reasoning.

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📚 Reference

1. Nikhil R. Pal, Kuhu Pal, James M. Keller, and James C. Bezdek (2005). A Possibilistic Fuzzy C-Means Clustering Algorithm, IEEE Transactions on Fuzzy Systems, DOI:10.1109/TFUZZ.2004.840845.