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SUMMARY:Formulations of community detection in terms of total variation an
 d surface tension - Zachary Boyd (University of California\, Los Angeles)
DTSTART:20171215T090000Z
DTEND:20171215T100000Z
UID:TALK96637@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Network data structures arise in numerous applications\, e.g. 
 in image segmentation when graph cut methods are used or in the form of a 
 similarity graph on the pixels in certain clustering methods. Networks als
 o occur as social\, biological\, technological\, and transportation networ
 ks\, for instance\, all of which are receiving a lot of attention right no
 w. "Community detection" is a body of techniques for extracting large- and
  medium-scale structure from such graphs. Most community detection formali
 zations turn out to be NP-hard and in practice are horrendously nonconvex.
  Practitioners from many fields are struggling to find formulations that (
 1) helpfully summarize the network data and (2) are computationally tracta
 ble. Most formulations have neither property.  In my talk\, I will give tw
 o examples of how existing community detection models can be understood in
  terms of objects familiar in image processing. The first example casts th
 e popular modularity heuristic as a graph total variation problem with a s
 oft area balance constraint. The second views the more flexible stochastic
  block model as a discrete surface tension minimization problem\, which in
  the two-community case is exactly equivalent to the first example.  These
  equivalences can potentially benefit both the network science community a
 nd the image processing community by allowing tools from one domain to be 
 applied to the other. As an example\, I show how mean curvature flow\, pha
 se field\, and threshold dynamics approaches to continuum total variation 
 minimization can be adapted to community detection in graphs\, including n
 onlocal means graphs for hyperspectral images and videos. The positive res
 ults hint that the methods commonly used in image processing can be readil
 y applied to much more general problems involving arbitrary graph structur
 es. I will also mention some possible future work in the reverse direction
 \, where I would like to bring methods from the network science literature
  into image processing.  This is joint work with Egil Bae\, Andrea Bertozz
 i\, Mason Porter\, and Xue-Cheng Tai.
LOCATION:Seminar Room 1\, Newton Institute
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