RW kernels, spanning forests and multiscale analysis on graphs.
par
Luca Avena
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Europe/Paris
Fokko du Cloux (La Doua, ICJ, Bât. Braconnier)
Fokko du Cloux
La Doua, ICJ, Bât. Braconnier
Description
We use ideas from large-scale stochastic dynamics to build a
multiresolution scheme to analyse arbitrary functions on graphs. These
types of problems emerge naturally in the context of signal processing.
The goal is to obtain successive approximations at different scales of
arbitrary functions on graphs which are used for signal classification,
reconstruction and data compression.When the signal is defined on a
graph having enough regularity structures, several methods (such as
wavelets) are available in the literature and used in practice. When the
regularity structure of the graph is lacking, very few methods are
known.Our work aims at addressing this issue by using random spanning
forests, loop-erased walks, determinantal structures, random walk
kernels and intertwining of Markov chains.
Joint work with Castel, Gaudilliere and Melot.