Spectral Clustering uses the eigenvalues of the similarity matrix of data to reduce their dimensionality and thus cluster them in a low dimensional manifold. It relates to graph theory and the concept of identifying groups of nodes based on the edges connecting them. Spectral Clustering is useful when the structure of a cluster is highly non-convex, or when a measure of the center and spread of a cluster does not describe a complete cluster. This happens, for example, when clusters are nested circles on a 2D plane.

Image From: Murphy, K. P. (2021). Figure 25.11. In Machine Learning: A Probabilistic Perspective. textbook, MIT Press.