| Abstract |
We present novel ideas and constructions that allow the
multiscale organization of graphs and data sets. These constructions are
based on ideas related to diffusions on data set, and use different time
and space scales associated with diffusion to infer multiscale
hierarchical organizations of a graph. They allow to generalize Fourier
and wavelet analysis to graphs and manifolds. They allow to organize
complex data sets and to generalize important signal processing tools to
graphs. In order to emphasize the wide applicability of these
techniques we will touch upon their applications to the organization of
document corpora, dimensionality reduction for dynamical systems,
nonlinear image denoising, reinforcement and semi-supervised learning. |
