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SUMMARY:Signal processing and random walks on simplicial complexes
DTSTART:20200225T161500
DTSTAMP:20260510T064945Z
UID:d65034083fc6b5940f86ddd5a8bde339b42fd05eb0f44c5dc1dbcc2a
CATEGORIES:Conferences - Seminars
DESCRIPTION:Michael Schaub\nIn many applications\, we are confronted with 
 with signals defined on the nodes of a graph.\nThink for instance of a sen
 sor network measuring temperature\; or a social network\, in which each pe
 rson has an opinion about a specific issue.\nGraph signal processing (GSP)
  tries to device appropriate tools to process such data by generalizing cl
 assical methods from signal processing of time-series and images — such 
 as smoothing\, filtering and interpolation — to signals defined on graph
 s.\nTypically\, this involves leveraging the structure of the graph as enc
 oded in the spectral properties of the graph Laplacian.\nIn applications s
 uch as traffic network analysis\, however\, the signals of interest are na
 turally defined on the edges of a graph\, rather than on the nodes.\nAfter
  a brief introduction to the ideas of GSP\, we examine why the standard to
 ols from GSP may not be suitable for the analysis of such edge signals.\nM
 ore specifically\, we discuss how the underlying notion of a ‘smooth sig
 nal’ inherited from (the typically considered variants of) the graph Lap
 lacian are not suitable when dealing with edge signals that encode a notio
 n of flow.\nTo overcome this limitation we devise signal processing tools 
 based on the Hodge 1-Laplacian and discrete Hodge Theory.\nWe first discus
 s how these tools can be applied for signal smoothing\, semi-supervised an
 d active learning for edge-signals on graphs.\nWe then explore connections
  of these signal processing tools to random walks on graphs and simplicial
  complexes\, and give alternative interpretations of our previously derive
 d methods in terms of diffusion processes on simplicial complexes.\n\nSpea
 ker: Michael Schaub\, University of Oxford\n\nMore information can be foun
 d on the seminar's webpage: https://www.epfl.ch/labs/hessbellwald-lab/sem
 inar/apptopsem1920/
LOCATION:MA B2 485 https://plan.epfl.ch/?room==MA%20B2%20485
STATUS:CONFIRMED
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