ECM (Evidential C-Means) Documentation

🔍 Overview

ECM is an evidential extension of the classic Fuzzy C-Means algorithm. It is based on the theory of belief functions and produces a credal partition. Each data point can belong to multiple clusters or even be assigned to the ignorance/noise cluster if its assignment is uncertain.

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⚙️ Class Definition

Class Name: ECM This class implements the ECM clustering algorithm using mass assignment and credal partitions.

class ECM:
    def __init__(self, n_clusters: int = 3, m: float = 2.0, delta: float = 10.0, max_iter: int = 100, tol: float = 1e-5):
        ...

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📋 Parameters

Parameter	Type	Default	Description
n_clusters	int	3	Number of clusters
m	float	2.0	Fuzziness degree
delta	float	10.0	Distance threshold for the noise cluster
max_iter	int	100	Maximum number of iterations
tol	float	1e-5	Convergence threshold based on centroid changes

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🚀 Usage Examples

from soft_clustering._ecm._ecm import ECM
import numpy as np

X = np.array([
    [1.0, 2.0],
    [1.5, 1.8],
    [5.0, 8.0],
    [8.0, 8.0],
    [1.0, 0.6],
    [9.0, 11.0]
])

model = ECM(n_clusters=2, m=2.0, delta=5.0, max_iter=100)
model.fit(X)
mass = model.get_membership()

print("Mass matrix:")
print(mass)

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📥 Input / 📤 Output

• Input to fit(X):

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

• Returns:

  • Mass matrix (N x K+1), where the last column is for the noise cluster

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🛠️ Methods

• fit(X): Runs the ECM algorithm and updates prototypes and mass matrix

• get_membership(): Returns the learned mass matrix including noise cluster

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📝 Implementation Notes

• Mass values are normalized for each sample

• A noise cluster is modeled using a fixed distance delta

• Memberships are expressed as belief degrees, not just probabilities

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📚 Reference

This implementation is based on:
“ECM: An Evidential Version of the Fuzzy C-Means Algorithm”
by T. Denoeux, M. Masson (2004).