Stefan Steinerberger, Yale University, Parabolic equations, expanders, t-SNE and data analysis

Beschreibung

I will discuss two recent widely used algorithms in data analysis (after introducing them, no knowledge necessary). The emphasis is on mathematical ideas, not on algorithms or applications. (1) Spectral Clustering is based on building graphs on the data and use the Laplacian Eigenfunctions as intrinsic coordinates. One problem in practice is that building a graph is expensive. We discuss novel probabilistic/combinatorial technique that relate to expander graphs and percolation theory that yield much \lq\lq better" graphs than commonly used constructions. Joint work with G. Linderman, G. Mishne and Y. Kluger. (2) t-SNE is a way to visualize massive amounts of data as nice little clouds in $\mathbf R^2$. It is THE standard visualization technique in biosciences (citation count $>$ 3000). Despite this, no mathematical theory existed. I will present an interpretation of the algorithm as the evolution of a uniformly parabolic discrete system with large noise -- this proves convergence and, what's really nice, tells you how to make the algorithm much better. Joint work with G. Linderman.

Zeitraum	29 Dez. 2017
Veranstaltungstyp	Gastvortrag
Ort	ÖsterreichAuf Karte anzeigen