Understanding big data spectral clustering

This article introduces an original approach to understand the behavior of standard kernel spectral clustering algorithms (such as the Ng-Jordan-Weiss method) for large dimensional datasets. Precisely, using advanced methods from the field of random matrix theory and assuming Gaussian data vectors, we show that the Laplacian of the kernel matrix can asymptotically be well approximated by an analytically tractable equivalent random matrix. The study of the latter unveils the mechanisms into play and in particular the impact of the choice of the kernel function and some theoretical limits of the method. Despite our Gaussian assumption, we also observe that the predicted theoretical behavior is a close match to that experienced on real datasets (taken from the MNIST database).