# Applications of polar decomposition in Machine Learning

Assume there exists a new and very efficient algorithm for calculating the polar decomposition of a matrix $$A=UP$$, where $$U$$ is a unitary matrix and $$P$$ is a positive-semidefinite Hermitian matrix. Would there be any interesting applications in Machine Learning? Maybe topic modeling? Or page ranking? I am interested in references to articles and books.

• Hi and welcome to AI SE! Maybe have a look at geometric deep learning. There are some models there that make use of adjacency matrices and other matrices.
– nbro
May 20, 2020 at 16:25
• Thank you @nbro. Do you have any references I could check out? May 21, 2020 at 17:04
• Off the top of my head, I don't have a specific reference on GDL that talks about adjacency matrices (because it's been a while since I had to deal with GDL), but I guess that many papers on graph neural networks will talk about it. Maybe ask another question on the site about it. And I (or someone else) will try to provide a more formal answer.
– nbro
May 21, 2020 at 17:11