MATLAB Implementation of Spectral Clustering with K-means Comparison

This article presents a comprehensive MATLAB implementation of spectral clustering algorithm, including a complete k-means algorithm implementation for comparison. Spectral clustering represents an advanced clustering methodology that generally outperforms conventional k-means in terms of clustering accuracy and data separation quality. The implementation covers key algorithmic components including affinity matrix construction using Gaussian kernel similarity measures, graph Laplacian computation with normalization options, eigenvalue decomposition for dimensionality reduction, and final clustering using k-means in the reduced spectral space. Notably, spectral clustering excels at identifying non-convex clusters and handling complex data distributions that challenge traditional k-means approaches. Through MATLAB's built-in functions for matrix operations (eig, eigs) and custom implementations for similarity calculations, readers can observe how spectral clustering more effectively captures the underlying data structure. The code includes practical considerations for parameter selection, such as sigma value tuning for the similarity matrix and optimal cluster number determination using eigenvalue gaps. We also explore practical application scenarios where spectral clustering demonstrates particular strength, including image segmentation, social network analysis, and biological data clustering. The MATLAB implementation provides modular components that allow easy adaptation to various data types and clustering requirements. By studying this implementation, readers will gain deeper insights into spectral clustering's theoretical foundations and develop practical skills for applying these techniques to real-world data analysis challenges, leveraging MATLAB's computational efficiency for handling large-scale clustering problems.