AFCM (Without Graph Embedding) Documentation

🔍 Overview

This version of Adaptive Fuzzy C-Means (AFCM) performs clustering by adaptively updating fuzzy memberships and cluster centers, without incorporating any graph structure. It is a simplified form of the full AFCM model and operates directly on the original data space.

---

⚙️ Class Definition

Class Name: AFCMSIMPLE

This class implements the simplified AFCM model with adaptive fuzzy memberships and convergence control.

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

---

📋 Parameters

Parameter	Type	Default	Description
c	int	—	Number of clusters
m	float	2.0	Fuzziness degree
max_iter	int	100	Maximum number of iterations
tol	float	1e-5	Tolerance for convergence

---

🚀 Usage Examples

from soft_clustering._afcm_simple._afcm_simple import AFCMSimple
import numpy as np

X = np.vstack([
    np.random.normal(loc=[0, 0], scale=0.5, size=(50, 2)),
    np.random.normal(loc=[3, 3], scale=0.5, size=(50, 2)),
])

model = AFCMSimple(c=2)
labels, U = model.fit_predict(X)

print("Cluster Labels:", labels)
print("Membership Matrix:", U)

---

📥 Input / 📤 Output

• Input to fit_predict(X):

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

• Returns:

  • labels (np.ndarray): Final hard cluster assignments (N,)

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

---

🛠️ Methods

• __init__(self, c, m=2.0, max_iter=100, tol=1e-5): Initializes the model with cluster count and training options.

• fit_predict(self, X): Learns fuzzy memberships and returns both final labels and the U matrix.

---

📝 Implementation Notes

• This version does not include graph embedding or regularization terms.

• It iteratively updates fuzzy memberships and centers until convergence.

• Suitable for data without known manifold structure or graph connectivity.

---

📚 Reference

This implementation is based on: “Adaptive Fuzzy C-Means with Graph Embedding”,
but applies the simplified version without Laplacian constraints.