🔍 Spectral Clustering on Synthetic Datasets

This project demonstrates the use of Spectral Clustering implemented in MATLAB, applied to synthetic datasets including circular, spherical, and spiral patterns. The goal is to cluster non-linearly separable data using graph-based clustering methods.

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📁 Project Structure

.
├── data/
│   ├── Circle.csv
│   ├── Sphere.csv
│   └── Spiral.csv
├── report/
│   └── spectral_clustring_report.pdf
├── src/
│   └── spectral_clustring.m
└── instruction.txt

• data/: Contains the datasets in .csv format.
• src/: MATLAB implementation of the Spectral Clustering algorithm.
• report/: Detailed PDF report explaining the methodology, implementation, and results.
• instruction.txt: Additional project instructions.

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📌 Features

• Spectral clustering with adjacency and Laplacian matrix construction.
• Works on complex shapes like spirals and rings.
• Eigen decomposition-based dimensionality reduction.
• K-means clustering on spectral embedding.
• Evaluation with plots and visualizations.

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Algorithm Overview

1. Load Data from CSV files.
2. Build Similarity Graph using distance-based metrics.
3. Compute Laplacian Matrix.
4. Extract Eigenvectors of the Laplacian.
5. Apply K-means to cluster eigenvector representation.
6. Visualize Results for each dataset.

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🛠 Dependencies

• MATLAB (tested on R2024a and R2024b)
• No additional toolboxes required

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📄 Report

See report/spectral_clustring_report.pdf for methodology, visuals, and analysis.

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📜 License

This project is licensed under the MIT License.