FCC (Fuzzy Color Clustering) Documentation

🔍 Overview

Fuzzy Color Clustering (FCC) is a color clustering algorithm that represents each cluster as a fuzzy color sphere in CIELAB space. Each data point (color) has a degree of membership in each cluster, based on its distance from the fuzzy centroid using a JND (Just Noticeable Difference) threshold.

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⚙️ Class Definition

Class Name: FCC This class implements the Fuzzy Color Clustering model.

class FCC:
    def __init__(self, c: int, jnd: float = 20.0, max_iter: int = 100, tol: float = 1e-5):
        self.c = c
        self.jnd = jnd
        self.max_iter = max_iter
        self.tol = tol

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📋 Parameters

Parameter	Type	Default	Description
c	int	—	Number of clusters
jnd	float	20.0	Radius of fuzzy sphere (Just Noticeable Difference)
max_iter	int	100	Maximum number of iterations
tol	float	1e-5	Convergence threshold for centroid updates

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🚀 Usage Examples

from soft_clustering._fcc._fcc import FCC
import numpy as np

# Generate synthetic CIELAB colors
X = np.vstack([
    np.random.normal(loc=[50, 20, 20], scale=5.0, size=(50, 3)),
    np.random.normal(loc=[70, -10, 30], scale=5.0, size=(50, 3))
])

model = FCC(c=2, jnd=20.0)
labels, U = model.fit_predict(X)

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

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📥 Input / 📤 Output

• Input to fit_predict(X):

  • X (np.ndarray): Matrix of shape (N x 3) with color data in CIELAB space

• Returns:

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

  • U (np.ndarray): Membership matrix with fuzzy degrees (N x C)

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🛠️ Methods

• __init__(...): Initializes the FCC model with number of clusters and fuzzy radius

• fit_predict(X): Performs the clustering algorithm and returns both hard and soft results

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📝 Implementation Notes

• Distance is calculated in CIELAB space (Euclidean)

• If a color is inside the fuzzy sphere → membership = 1

• Else → membership is computed with inverse of excess distance

• Memberships are normalized across clusters

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📚 Reference

This implementation is based on:
“Fuzzy Color Model and Clustering Algorithm for Color Clustering”
by A. Kovács and J. Abonyi.