Rough K-Means (RoughKMeans)

A clustering method where points can belong to multiple clusters, and centers are updated using both definite and possible members.

🔍 Overview

RoughKMeans is a clustering algorithm based on rough-set theory. Instead of assigning each sample to exactly one cluster, it defines:

Lower approximation (L): samples that definitely belong to a cluster.
Upper approximation (U): samples that possibly belong to a cluster (including the lower set).

It computes per-cluster thresholds (alpha and beta) to distinguish core vs. fringe members, then updates cluster centroids by mixing core and fringe means.

⚙️ Class Definition

class rough_kmeans.RoughKMeans(
    n_clusters: int = 2,
    weight_lower: float = 0.7,
    max_iter: int = 100,
    tol: float = 1e-4
)

🔗 Source on GitHub

📋 Parameters

Parameter	Type	Default	Description
n_clusters	`int`	`2`	Number of clusters to form.
weight_lower	`float`	`0.7`	Weight for averaging between lower and fringe regions when updating means.
max_iter	`int`	`100`	Maximum number of iterations for convergence.
tol	`float`	`1e-4`	Tolerance for centroid movement to declare convergence.

🚀 Usage Examples

from soft_clustering import RoughKMeans
import numpy as np

# Create sample dataset
X = np.array([
    [1.0, 2.0],
    [1.2, 1.9],
    [0.8, 2.1],
    [8.0, 8.0],
    [8.2, 7.8],
    [7.9, 8.3]
])

# Initialize and fit the model
model = RoughKMeans(n_clusters=2, weight_lower=0.6, max_iter=50, tol=1e-3)
results = model.fit_predict(X)

print("Lower approximation:\n", results['lower_approx'])
print("Upper approximation:\n", results['upper_approx'])
print("Centroids:\n", results['centroids'])
print("Iterations:", results['n_iter'])

🛠️ Methods

`fit_predict(X)`

Perform Rough K-Means clustering using interval-set approximations.

Parameters:

X (np.ndarray, shape (n_samples, n_features)): Feature matrix of input data.

Returns:

result (dict) with:

lower_approx (np.ndarray, shape (n_samples, n_clusters)): Binary matrix indicating definite membership.

upper_approx (np.ndarray, shape (n_samples, n_clusters)): Binary matrix indicating possible membership.

centroids (np.ndarray, shape (n_clusters, n_features)): Final cluster centers.

n_iter (int): Total number of iterations executed.

🔗 Source definition

📝 Implementation Notes

Centroid Initialization: Centroids are randomly initialized from the dataset.

📚 Reference

Lingras, P., & West, C. (2004). Interval Set Clustering of Web Users with Rough K-Means. Journal of Intelligent Information Systems, 23(1), 5-16.(https://link.springer.com/article/10.1023/B:JIIS.0000029668.88665.1a)