CAF-HFCM (Centroid Auto-Fused Hierarchical FCM) Documentation

🔍 Overview

CAFHFCM is a fuzzy clustering algorithm that integrates traditional FCM with a centroid fusion regularization. The method promotes centroid merging by minimizing both distance-to-centroid loss and an L2 penalty encouraging centroid similarity.

⚙️ Class Definition

Class Name: CAFHFCM This class implements the Centroid Auto-Fused Hierarchical FCM clustering algorithm.

class CAFHFCM:
    def __init__(self, c: int, m: float = 2.0, alpha: float = 0.1,
                 max_iter: int = 100, tol: float = 1e-5):
        self.c = c
        self.m = m
        self.alpha = alpha
        self.max_iter = max_iter
        self.tol = tol

📋 Parameters

Parameter	Type	Default	Description
`c`	int	—	Number of clusters
`m`	float	2.0	Fuzziness coefficient
`alpha`	float	0.1	Fusion regularization weight
`max_iter`	int	100	Maximum number of iterations
`tol`	float	1e-5	Tolerance for centroid convergence

🚀 Usage Examples

from soft_clustering._cafhfcm._cafhfcm import CAFHFCM
import numpy as np

X = np.vstack([
    np.random.normal(loc=[1, 1], scale=0.5, size=(50, 2)),
    np.random.normal(loc=[5, 5], scale=0.5, size=(50, 2))
])

model = CAFHFCM(c=2, m=2.0, alpha=0.1)
labels, memberships = model.fit_predict(X)

print("Labels:", labels)
print("Memberships:", memberships)

📥 Input / 📤 Output

Input to fit_predict(X):
- X (np.ndarray): Input data of shape (N x D)
Returns:
- labels (np.ndarray): Hard cluster labels (N,)
- U (np.ndarray): Soft membership matrix (N x C)

🛠️ Methods

__init__(...): Initializes the model
fit_predict(X): Runs the CAFHFCM algorithm and returns labels and memberships

📝 Implementation Notes

The algorithm updates membership matrix and centroids iteratively
The centroid update includes a penalty for centroid differences
Promotes centroid fusion when data distribution is hierarchical

📚 Reference

This implementation is based on:
“A Centroid Auto-Fused Hierarchical Fuzzy c-Means Clustering”
by L. Yu, Y. Pan, J. Wu, and J. Zhao.