In the first set of tutorials, we looked at the behavior of random walks on graphs for large time. Here we focus on multiscale analysis of and on graphs: it is possible to look at a random walk at all possible time scales in a coherent multiscale fashion, that corresponds to creating wavelets on graphs. We discuss the geometric aspects, which correspond to a geometric compression of graphs, as well as the analysis aspects, corresponding to a wavelet analysis of functions on graphs. We discuss applications to machine learning and organization of large data sets.
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