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UID:2008@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20171117T133000
DTEND;TZID=Europe/Paris:20171117T143000
DTSTAMP:20171102T123000Z
URL:https://www.i2m.univ-amu.fr/evenements/intertwinning-wavelets-or-multi
 resolution-analysis-on-graphs-through-random-forests/
SUMMARY: (...): Intertwinning wavelets or multiresolution analysis on graph
 s through random forests
DESCRIPTION:: Several methods are available to analyze signals on graphs\, 
 i.e functions defined on the vertices of a finite connected weighted graph
 . Fourier analysis requires the computation of the eigenvalues and eigenve
 ctors of the graph Laplacian\, it is also a non-local transformation. In t
 his talk we will propose a multiresolution scheme which provides well loca
 lized basis functions without requiring spectral computations.Our approach
  relies on a random spanning forest to downsample the set of vertices\, an
 d on approximate solutions of Markov intertwining relation to provide a su
 bgraph structure\, and a filter bank \, leading to a wavelet basis of the 
 set of functions. Our construction involves two parameters q and q′. The
  first one controls the mean number of kept vertices in the downsampling\,
  while the second one is a tuning parameter between space localization and
  frequency localization. Even if our basis functions are well localized\, 
 they are not orthonormal but we can provide an explicit reconstruction for
 mula\, bounds on the reconstruction operator norm\, on the error in the in
 tertwining relation\, and a Jackson-like inequality. These bounds lead to 
 recommend a way to choose the parameters q and q′. We illustrate the met
 hod by numerical experiments.Webpage
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DTSTART:20171029T020000
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