Body: <p>Assume there exists a new and very efficient algorithm for calculating the polar decomposition of a matrix <span class="math-container">$A=UP$</span>, where <span class="math-container">$U$</span> is a unitary matrix and <span class="math-container">$P$</span> 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.</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2020-05-20T16:25:41.870Z
Comments.Text: 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.
Comments.UserDisplayName: nbro
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2020-05-21T17:04:31.063Z
Comments.Text: Thank you @nbro. Do you have any references I could check out?
Comments.UserDisplayName: Samuel
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2020-05-21T17:11:12.520Z
Comments.Text: 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.
Comments.UserDisplayName: nbro
Tags: <machine-learning><graphs><text-classification><semantics><singular-value-decomposition>
Title: Applications of polar decomposition in Machine Learning
UserDisplayName: Samuel
ThreadText: # Applications of polar decomposition in Machine Learning
  
  (Asked by: username_0 on 2020-05-19)
  
  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.
  
  **Tags:** machine-learning, graphs, text-classification, semantics, singular-value-decomposition
  > **Comments:**
  > **username_1**: 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.  
  > **username_0**: Thank you @nbro. Do you have any references I could check out?  
  > **username_1**: 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.  
  
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