Dataset comparison using persistent homology morphisms

Date(s): Wednesday 31st May 2023 (10:00-11:00)
Contact: Event Convenor Contact: A.M.Kasprzyk@nottingham.ac.uk
Description: Speaker's Name: Alvaro Torras Casas
Speaker's Affiliation: Cardiff
Speaker's Research Theme(s): Symbolic computational mathematics,Computational statistics and machine learning
Abstract:
Persistent homology summarizes geometrical information of data by means of a barcode. Given a pair of datasets, X and Y, one might obtain their respective 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. In 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 is a sample taken from Y. As in linear algebra, a morphism between persistence 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 barcodes for images, kernels and cokernels. Additionally, I will explain how to 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.

Venue: Zoom
Online Conference Link: https://us06web.zoom.us/j/81652314055?pwd=YjlJUFlpL3lJT0R1ZEdrclZvSEFidz09

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