EntropyFCM (Entropy c-Means) Documentation

🔍 Overview

Entropy c-Means (EntropyFCM) is a fuzzy clustering algorithm designed to balance between compact clusters and fuzzy membership distributions. The objective function optimizes both compactness and entropy of membership values, allowing flexible cluster boundaries based on user-defined weighting.

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⚙️ Class Definition

Class Name: EntropyFCM This class implements the EntropyFCM algorithm, supporting soft clustering with entropy regularization.

class EntropyFCM:
    def __init__(self, c: int, m: float = 2.0, entropy_weight: float = 1.0,
                 max_iter: int = 100, tol: float = 1e-5):
        self.c = c
        self.m = m
        self.entropy_weight = entropy_weight
        self.max_iter = max_iter
        self.tol = tol

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📋 Parameters

Parameter	Type	Default	Description
c	int	—	Number of clusters
m	float	2.0	Fuzziness degree
entropy_weight	float	1.0	Weight of the entropy regularization term
max_iter	int	100	Maximum number of iterations
tol	float	1e-5	Convergence threshold for centroid changes

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🚀 Usage Examples

from soft_clustering._EntropyFCM._EntropyFCM import EntropyFCM
import numpy as np

X = np.vstack([
    np.random.normal(loc=[0, 0], scale=0.4, size=(40, 2)),
    np.random.normal(loc=[3, 3], scale=0.4, size=(40, 2))
])

model = ECM(c=2, m=2.0, entropy_weight=1.0)
labels, memberships = model.fit_predict(X)

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

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📥 Input / 📤 Output

• Input to fit_predict(X):

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

• Returns:

  • labels (np.ndarray): Hard labels assigned to each point

  • U (np.ndarray): Fuzzy membership matrix (N x C)

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🛠️ Methods

• __init__(...): Initializes the model and sets parameters

• fit_predict(X): Runs the clustering algorithm and returns both labels and memberships

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📝 Implementation Notes

• Memberships initialized using a Dirichlet distribution

• Objective balances compactness (distance to centroids) and entropy

• Entropy encourages fuzzy, overlapping memberships when needed

• Convergence based on stability of centroid positions

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📚 Reference

This implementation is based on:
“Fuzzy Clustering to Identify Clusters at Different Levels of Fuzziness”
by Miguel A. Carreira-Perpiñán and Weiran Wang.