Geometric Structures seminar - Tim Laux - June 27, 2022 - 4:00 pm (Rome Time)

[Miruna - Stefana Sorea]

Dear All,

This is a reminder of today's seminar from the series "Geometric Structures".
Please note that the seminar will exceptionally take place today, June 27th, at 4:00 pm (Rome Time).

Speaker: Tim Laux<https://math.berkeley.edu/~tim.laux/index.html> (Hausdorff Center for Mathematics in Bonn)

Title: The large-data limit of the MBO scheme for data clustering

Time: June 27, 2022, 4:00 pm (Rome Time)
Venue: room 134* (*to be confirmed)
on zoom at this link:
https://sissa-it.zoom.us/j/85675591787?pwd=TUo2VXpmcEhOU1paRzBXUWp2MU1odz09
Passcode: geometry

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Abstract:
The MBO scheme is an efficient scheme used for data clustering, the task of partitioning a given dataset into several clusters. In this talk, I will present a rigorous analysis of the MBO scheme for data clustering in the large-data limit. Each iteration of the MBO scheme corresponds to one step of implicit gradient descent for the thresholding energy on the similarity graph of the dataset. For a subset of the nodes of the graph, the thresholding energy is the amount of heat transferred from the subset to its complement. It is then natural to think that outcomes of the MBO scheme are (local) minimizers of this energy. We prove that the algorithm is consistent, in the sense that these (local) minimizers converge to minimizers of a suitably weighted optimal partition problem. This is joint work with Jona Lelmi (U Bonn).

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Miruna-Stefana Sorea
Postdoctoral Researcher
Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste, Italy
https://sites.google.com/view/mirunastefanasorea/