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.