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SUMMARY:Henry Adams (Colorado State University)
DTSTART:20200602T230000Z
DTEND:20200603T001500Z
DTSTAMP:20260423T004656Z
UID:MADDD/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MADDD/6/">Ap
 plied topology: From global to local.</a>\nby Henry Adams (Colorado State 
 University) as part of Mathematics of Data and Decisions @ Davis\n\n\nAbst
 ract\nThrough the use of examples\, I will explain one way in which applie
 d topology has evolved since the birth of persistent homology in the early
  2000s. The first applications of topology to data emphasized the global s
 hape of a dataset\, such as the three-circle model for 3 x 3 pixel patches
  from natural images\, or the configuration space of the cyclo-octane mole
 cule\, which is a sphere with a Klein bottle attached via two circles of s
 ingularity. More recently\, persistent homology is being used to measure t
 he local geometry of data. How do you vectorize geometry for use in machin
 e learning problems? Persistent homology\, and its vectorization technique
 s including persistence landscapes and persistence images\, provide popula
 r techniques for incorporating geometry in machine learning. I will survey
  applications arising from machine learning tasks in agent-based modeling\
 , shape recognition\, archaeology\, materials science\, and biology.\n
LOCATION:https://researchseminars.org/talk/MADDD/6/
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