Applied Math Distinguished Lecture | Andrea Bertozzi, Geometric Graph-Based Methods for High Dimensional Data

Thursday, April 8, 2021 2:30 pm - 2:30 pm EDT (GMT -04:00)

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Speaker

Andrea Bertozzi Ìý| University of California

Title

Geometric Graph-Based Methods for High Dimensional Data

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High dimensional data can be organized on a similarity graph - anÌýundirected graph with edge weights that measure the similarity between data assigned to nodes.ÌýWe consider problems in semi-supervised and unsupervised machine learningÌýthat are formulated as penalized graph cut problems. There are a wideÌýrange of problems including Cheeger cuts, modularity optimization onÌýnetworks, and semi-supervised learning.ÌýWe show a parallel between these modern problems and classical minimalÌýsurface problems in Euclidean space. Ìý

This analogy allows us to develop a suite of new algorithms for machine learning that are both very fast andÌýhighly accurate. ÌýThese are analogues of well-known pseudo-spectralÌýmethods for partial differential equations.