spectral-clustering-demo: Spectral Clustering Algorithm Implementation

Spectral clustering is a graph theory-based clustering algorithm particularly suitable for handling non-linearly separable datasets. Unlike traditional algorithms like K-means, spectral clustering utilizes the similarity matrix of data and achieves dimensionality reduction and clustering through eigen decomposition of the graph Laplacian matrix. This MATLAB demonstration program implements both the classical N-cut method and its improved version. The N-cut (Normalized Cut) method minimizes the normalized cost function of graph partitioning, enabling better balance between cluster sizes. The improved N-cut version incorporates optimizations in similarity matrix computation or feature selection, enhancing both clustering performance and computational efficiency. The demo enables users to visually understand core spectral clustering steps: constructing similarity matrices using functions like pdist2 for distance calculation, computing Laplacian matrices with normalization techniques, performing eigen decomposition via eigs function for efficient sparse matrix handling, and applying K-means clustering to the selected eigenvectors. The debugged code includes practical implementations of Gaussian similarity functions and eigenvalue threshold selection, making it directly executable for learners while providing deep insights into mathematical principles and implementation details. For researchers and engineers seeking to master spectral clustering, this resource serves as an excellent learning foundation. It demonstrates practical MATLAB code translation of theoretical concepts and provides reference points for optimization approaches, including efficient matrix operations and parameter tuning strategies for real-world applications.