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SUMMARY:Clustering of Big Data: consistency of a nonlocal Ginzburg-Landau 
 type model - Riccardo Cristoferi\, Heriot-Watt University
DTSTART:20190301T160000Z
DTEND:20190301T170000Z
UID:TALK120937@talks.cam.ac.uk
CONTACT:Yury Korolev
DESCRIPTION:The analysis of Big Data is one of the most important challeng
 es of the modern era. A first step in order to extract some information fr
 om a set of data is to partition it according to some notion of similarity
 . When only geometric features are used to define such a notion of similar
 ity and no a priori knowledge of the data is available\, we refer to it as
  the clustering problem.\n\nTypically this labelling task is fulfilled via
  a minimization procedure. Of capital importance for evaluating a clusteri
 ng method is whether it is consistent or not\; namely it is desirable that
  the minimization procedure approaches some limit minimization method when
  the number of elements of the data set goes to infinity.\n\nIn this talk 
 the consistency of a nonlocal anisotropic Ginzburg-Landau type functional 
 for clustering is presented. In particular\, it is proved that the discret
 e model converges\, in the sense of Gamma-convergence\, to a weighted anis
 otropic perimeter.\n\nThe talk is based on a work in collaboration with Ma
 tthew Thorpe (Cambridge University).
LOCATION:MR 11\, Centre for Mathematical Sciences
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