Spectral Clustering Explained: How Eigenvectors Reveal Complex Cluster Structures

Spectral clustering is a machine learning technique that can identify complex, non-linear cluster structures where algorithms like K-means often fail. The process involves constructing a similarity graph from the data points and then deriving a Laplacian matrix. Eigendecomposition is performed on this Laplacian matrix, and the resulting eigenvectors reveal the underlying cluster structure. These eigenvectors are used to embed the data into a new, lower-dimensional feature space where the clusters become more separable. Finally, a simpler algorithm like K-means is applied to this new feature space to assign the final cluster labels.