SKFCM (Spatially-Constrained Kernelized Fuzzy C-Means) Documentation

🔍 Overview

SKFCM extends Kernelized Fuzzy C-Means (KFCM) by adding a spatial constraint that incorporates local neighborhood information into the clustering process. This makes it more robust to noise and suitable for image segmentation tasks like MRI.

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⚙️ Class Definition

Class Name: SKFCM

class SKFCM:
    def __init__(self, n_clusters: int = 3, m: float = 2.0, gamma: float = 1.0,
                 lambda_: float = 0.5, 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
gamma	float	1.0	Kernel coefficient for RBF
lambda_	float	0.5	Spatial constraint weight
max_iter	int	100	Maximum number of iterations
tol	float	1e-5	Tolerance for convergence

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🚀 Usage Examples

from soft_clustering._skfcm._skfcm import SKFCM
import numpy as np

image = np.zeros((50, 50))
image[:25, :] = 0.2
image[25:, :] = 0.8
image += np.random.normal(0, 0.05, image.shape)

X = image.reshape(-1, 1)
shape = image.shape

model = SKFCM(n_clusters=2, gamma=5.0, lambda_=0.8)
model.fit(X, shape)

labels = model.predict().reshape(shape)
membership = model.predict_proba().reshape(shape[0], shape[1], -1)

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📥 Input / 📤 Output

• Input to fit(X, shape):

  • X (np.ndarray): Flattened image data (N x 1)

  • shape (Tuple[int, int]): Original image shape (height, width)

• Returns:

  • predict() → Hard labels (H x W)

  • predict_proba() → Membership matrix reshaped to (H x W x C)

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🛠️ Methods

• fit(X, shape): Performs spatially-regularized clustering

• predict(): Returns hard cluster labels

• predict_proba(): Returns fuzzy membership degrees

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📝 Implementation Notes

• Uses RBF kernel to capture nonlinear structure

• Adds neighborhood averaging term via uniform filter

• More robust to noise and boundary fluctuations than KFCM

• Especially effective for image segmentation

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📚 Reference

1. Chen, S., & Zhang, D. (2004). A novel kernelized fuzzy C-means algorithm with application in medical image segmentation. Pattern Recognition Letters 25.