Matrix Completion using the Nuclear Norm for Low Rank Factorization

This video is a course project for EE5120 Applied Linear Algebra (Jul-Nov 2018) at IIT Madras. The goal of the video is to focus on the linear algebra aspects of the following paper, and use it to create recommendation systems for services like Netflix.
Ricardo Cabral, Fernando De la Torre, João P. Costeira, Alexandre Bernardino. Unifying Nuclear Norm and Bilinear Factorization Approaches for Low-rank Matrix Decomposition. 2013 IEEE International Conference on Computer Vision.
printart.isr.ist.utl.pt/ICCV13...
This is our implementation of the ALM method for optimization (Algorithm 1 in the paper):
github.com/rajatvd/EE5120_Video
References:
Emmanuel J. Candes and Benjamin Recht. Exact Matrix Completion via Convex Optimization.
arxiv.org/abs/0805.4471
Venkat Chandrasekaran, Benjamin Recht, Pablo A. Parrilo, and Alan S. Willsky. The Convex Geometry of Linear Inverse Problems.
arxiv.org/abs/1012.0621
Benjamin Recht, Maryam Fazel and Pablo A. Parrilo. Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization.
arxiv.org/abs/0706.4138
M. Fazel. Matrix Rank Minimization with Applications. PhD thesis, Stanford University, 2002.
faculty.washington.edu/mfazel...

[@psharpep]

Grad student at MIT watching this - cool example using the MIT logo! I've never thought of our logo as low-rank before, but now I'll always see it in a new way. Great explanation, thanks for posting the video!

[@dhruvpatel4948]

Super cool stuff! Low rank matrix appears everywhere in my research (on inverse problems) and this is an interesting combination of many known powerful methods. Will check out some of the references.

[@viktorajstein]

Is there a reason you write rank(Z*) instead of rank(Z) at 4:33?

[@robmarks6800]

Asteriks denote that it’s the Z with the lowest rank, i.e rank(Z*)

[@nobodyQAQ]

I'm surprised I see this

[@viktorajstein]

How so?

[@nobodyQAQ]

@@viktorajstein I am researching this