Spectral Clustering Demo - Implementation and Algorithm Analysis

Spectral clustering is a graph theory-based clustering algorithm that performs dimensionality reduction and clustering by utilizing the similarity matrix between data points. This MATLAB demonstration program provides learners with a complete implementation case of spectral clustering, particularly suitable for users who want to understand the core principles of the algorithm.

The program implements two key variants: the classic normalized cut (N-cut) method and an improved N-cut method. The N-cut method achieves more natural clustering results by optimizing graph partition criteria, while the improved version enhances computational efficiency and result stability. The demo showcases the complete process from constructing similarity matrices to final clustering results, including critical steps like Laplacian matrix computation and eigendecomposition. The code implementation demonstrates how to properly handle key operations such as similarity matrix construction using Gaussian kernel functions and eigenvalue decomposition using MATLAB's built-in eigs function.

Through this debugged demonstration program, learners can visually observe how spectral clustering handles non-linearly separable datasets and how different parameter settings affect final clustering results. The program's comments and implementation details help understand error-prone aspects of the algorithm, such as similarity matrix construction parameters (sigma value selection) and eigenvector selection criteria. The code includes practical considerations for handling numerical stability issues when computing graph Laplacians and selecting the appropriate number of eigenvectors for clustering.

For researchers or students who want to master spectral clustering implementation details, this resource serves as both learning material and a reference template for their own implementations. It specifically demonstrates how to transform theoretical mathematical formulas into practical executable code logic, serving as an excellent bridge between algorithm theory and engineering practice. The implementation showcases real-world coding techniques including data preprocessing, parameter optimization loops, and cluster assignment using k-means on eigenvectors.