Python implementation of the spectral clustering algorithm from:

"Automatic Determination of the Number of Clusters using Spectral Algorithms"
Guido Sanguinetti, Jonathan Laidler, and Neil D. Lawrence (2005)
IEEE Workshop on Machine Learning for Signal Processing

This package automatically determines the number of clusters in a dataset using spectral methods.

• Automatic cluster number detection
• Handles non-convex cluster shapes
• Scikit-learn compatible API
• Faithful implementation of the 2005 algorithm

git clone https://github.com/lawrennd/spectral.git
cd spectral
pip install -e .

pip install -e ".[examples]"

import numpy as np
from spectral import SpectralCluster

# Generate three concentric circles
theta = np.linspace(0, 2*np.pi, 100, endpoint=False)
X = np.vstack([
    np.column_stack([np.cos(theta), np.sin(theta)]),
    np.column_stack([2*np.cos(theta), 2*np.sin(theta)]),
    np.column_stack([3*np.cos(theta), 3*np.sin(theta)])
])

# Cluster with automatic number detection
clf = SpectralCluster(sigma=0.16)  # Standard RBF formula
clf.fit(X)
print(f"Found {clf.n_clusters_} clusters")  # Should find 3

Note on Sigma: This implementation uses the standard RBF formula exp(-d²/(2σ²)). The original MATLAB uses exp(-d²/σ). To convert: σ_python = sqrt(σ_matlab / 2). See documentation for details.

See the examples/ directory for Jupyter notebooks reproducing the paper's experiments:

• Three concentric circles
• Non-convex shapes (ear, swirls)
• Image segmentation
• Spectrogram clustering

If you use this software, please cite the original paper:

@inproceedings{sanguinetti2005automatic,
  title={Automatic Determination of the Number of Clusters using Spectral Algorithms},
  author={Sanguinetti, Guido and Laidler, Jonathan and Lawrence, Neil D},
  booktitle={IEEE Workshop on Machine Learning for Signal Processing},
  year={2005}
}

The original MATLAB implementation is preserved in the matlab/ directory for reference and validation.

BSD 3-Clause License

Page last modified on Fri Jan 5 12:55:17 GMT 2007 (MATLAB version)
Python version: 2026-02-08