# Talk by Johannes Lutzeyer: «Extending the Davis-Kahan theorem for the comparison of embedding spaces spanned by eigenvectors»

**Speaker:**Johannes Lutzeyer

**Location:**Room Henri Poincaré

**Date:**Tue, 4 Feb 2020, 14:30-15:30

Dr. Johannes Lutzeyer, new postdoctoral researcher in DaSciM, will give a presentation at 14:30 entitled: *Extending the Davis-Kahan theorem for the comparison of embedding spaces spanned by eigenvectors*

**Abstract:** In this talk I will introduce the Davis-Kahan theorem, which is commonly used to upper bound the distance of two embedding spaces. It often forms an essential part of consistency proofs of algorithms based on spectral graph embeddings and variants of principal component analysis (PCA). However, the Davis-Kahan theorem has several weaknesses, which is why work on it continues. In this talk I present an extended version of the Davis-Kahan theorem which addresses these weaknesses and give a few proof of concept examples such as covariance embedding spaces in the context of the PCA algorithm and graph shift operator embedding spaces in the context of the spectral clustering algorithm. The work presented is joint work with Andrew Walden.