Existing approaches to analyzing the asymptotics of graph Laplacians typically assume a well-behaved kernel function with smoothness assumptions. We remove the smoothness assumpti...
Given a sample from a probability measure with support on a submanifold in Euclidean space one can construct a neighborhood graph which can be seen as an approximation of the subm...
Matthias Hein, Jean-Yves Audibert, Ulrike von Luxb...
Given a set of n randomly drawn sample points, spectral clustering in its simplest form uses the second eigenvector of the graph Laplacian matrix, constructed on the similarity gra...
Ulrike von Luxburg, Olivier Bousquet, Mikhail Belk...
We present a generalized version of spectral clustering using the graph p-Laplacian, a nonlinear generalization of the standard graph Laplacian. We show that the second eigenvecto...
Abstract. The regularization functional induced by the graph Laplacian of a random neighborhood graph based on the data is adaptive in two ways. First it adapts to an underlying ma...