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SUMMARY:Alvaro Torras Casas (Cardiff)
DTSTART:20230531T090000Z
DTEND:20230531T100000Z
DTSTAMP:20260423T021031Z
UID:CompAlg/19
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CompAlg/19/"
 >Dataset comparison using persistent homology morphisms</a>\nby Alvaro Tor
 ras Casas (Cardiff) as part of Machine Learning Seminar\n\n\nAbstract\nPer
 sistent homology summarizes geometrical information of data by means of a 
 barcode. Given a pair of datasets\, $X$ and $Y$\, one might obtain their r
 espective barcodes $B(X)$ and $B(Y)$. Thanks to stability results\, if $X$
  and $Y$ are similar enough one deduces that the barcodes $B(X)$ and $B(Y)
 $ are also close enough\; however\, the converse is not true in general. I
 n this talk we consider the case when there is a known relation between $X
 $ and $Y$ encoded by a morphism between persistence modules. For example\,
  this is the case when $Y$ is a finite subset of euclidean space and $X$ i
 s a sample taken from $Y$. As in linear algebra\, a morphism between persi
 stence modules is understood by a choice of a pair of bases together with 
 the associated matrix. I will explain how to use this matrix to get barcod
 es for images\, kernels and cokernels. Additionally\, I will explain how t
 o compute an induced block function that relates the barcodes $B(X)$ and $
 B(Y)$. I will finish the talk revising some applications of this theory as
  well as future research directions.\n
LOCATION:https://researchseminars.org/talk/CompAlg/19/
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