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SUMMARY:Variational Methods and PDEs on Graphs with Applications in Da
 ta Processing and Machine Learning\; Dr. Daniel Tenbrinck (WWU Münste
 r)
UID:a109c8e2-0f4b-42d6-a6ad-8c00702653ef
DESCRIPTION:ABSTRACT: Graph-based methods have emerged as a promising 
 tool for many applications in machine learning and data processing. On
 e key feature of these methods is the possibility to incorporate nonlo
 cal relationships in the data rather than using only local neighborhoo
 ds. The recent trend in the literature is to translate well-studied va
 riational problems and PDEs to the graph setting and overcome hereby d
 rawbacks of classical approaches. In this talk we give a short introdu
 ction to the concept of partial difference equations on graphs and sho
 w that classical numerical discretization schemes can be embedded in a
  graph setting and thus be interpreted as special cases in a more gene
 ral framework. To give an example we discuss a family of graph p- and 
 ∞-Laplacians. We analyze the corresponding PDEs involving these oper
 ators which enable us to perform important processing steps\, such as 
 diffusion-based filtering and interpolation of data. Finally\, we demo
 nstrate the advantages of graph-based methods for different tasks in i
 mage and point cloud processing\, i.e.\, filtering\, segmentation\, in
 painting\, and machine learning. This is a joint joint work with A. El
 moataz\, Université de Caen\, France.
DTSTART:20180426T141500Z
DTEND:20180426T151500Z
LOCATION:H13
DTSTAMP:20260723T183958Z
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