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SUMMARY:Simplicial Mixture Models – Fitting topology to data
DTSTART:20200114T161500
DTEND:20200114T171500
DTSTAMP:20260407T042004Z
UID:d4a667bac87e79ffe27de24afaebf91328c9a2d38106169ebd321788
CATEGORIES:Conferences - Seminars
DESCRIPTION:James Griffin Coventry University\nSpeaker: James Griffin\, Co
 ventry University\n\nAbstract: Lines and planes can be fitted to data by 
 minimising the sum of squared distances from the data to the geometric obj
 ect.  But what about fitting objects from topology such as simplicial com
 plexes?  I will present a method of fitting topological objects to data u
 sing a maximum likelihood approach\, generalising the sum of squared dista
 nces.  A simplicial mixture model (SMM) is specified by a set of vertex p
 ositions and a weighted set of simplices between them.  The fitting proce
 ss uses the expectation-maximisation (EM) algorithm to iteratively improve
  the parameters. Remarkably\, if we allow degenerate simplices then any di
 stribution in Euclidean space can be approximated arbitrarily closely usin
 g a SMM with only a small number of vertices.  This theorem is proved usi
 ng a form of kernel density estimation on the n-simplex.\n\nInformation ab
 out time and place of the Applied Topology Seminar can be found on the web
 page: https://www.epfl.ch/labs/hessbellwald-lab/seminar/apptopsem1920/
LOCATION:MA B2 485 https://plan.epfl.ch/?room==MA%20B2%20485
STATUS:CONFIRMED
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