Topology, Geometry and Data Seminar - Hanbaek Lyu

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Hanbaek Lyu
April 9, 2019
4:10PM - 5:10PM
Location
Cockins Hall 240

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Add to Calendar 2019-04-09 16:10:00 2019-04-09 17:10:00 Topology, Geometry and Data Seminar - Hanbaek Lyu Title: Stable network observables via dynamic embedding of motifs Speaker: Hanbaek Lyu (UCLA) Abstract: We propose a novel framework for constructing and computing various stable network observables. Our approach is based on sampling a random homomorphism from a small motif of choice into a given network. Integrals of the law of the random homomorphism induces various network observables, which include well-known quantities such as homomorphism density and average clustering coefficient. We show that these network observables are stable with respect to renormalized cut distance between networks. For their efficient computation, we also propose two Markov chain Monte Carlo algorithms and analyze their convergence and mixing times. We demonstrate how our techniques can be applied to network data analysis, especially for hypothesis testing and hierarchical clustering, through analyzing both synthetic and real world network data. Joint work with Facundo Memoli and David Sivakoff. Seminar URL: https://tgda.osu.edu/ Cockins Hall 240 Department of Mathematics math@osu.edu America/New_York public
Description

Title: Stable network observables via dynamic embedding of motifs

SpeakerHanbaek Lyu (UCLA)

Abstract: We propose a novel framework for constructing and computing various stable network observables. Our approach is based on sampling a random homomorphism from a small motif of choice into a given network. Integrals of the law of the random homomorphism induces various network observables, which include well-known quantities such as homomorphism density and average clustering coefficient. We show that these network observables are stable with respect to renormalized cut distance between networks. For their efficient computation, we also propose two Markov chain Monte Carlo algorithms and analyze their convergence and mixing times. We demonstrate how our techniques can be applied to network data analysis, especially for hypothesis testing and hierarchical clustering, through analyzing both synthetic and real world network data.

Joint work with Facundo Memoli and David Sivakoff.

Seminar URLhttps://tgda.osu.edu/

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