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I am not really a math guru myself, but I know that many estimation or approximation problems can be reformulated as minimizing the rank of a matrix. Although that is really hard, we can try to minimize the nuclear norm instead, which turns out to be a convex optimization problem that is easier to solve.

Let's say I have a sparse matrix X which I need to fill and somehow I've found the minimal nuclear norm. How can I impute the missing values now? And how the whole idea of minimizing the rank relate to that? Can you provide me with a simple(visual, if possible) example, please?

Rodrigo de Azevedo
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MLearner
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  • If you know that the matrix has low rank that puts more constraints on how the entries relate to each other. As a simple example, if you know that two rows must sum up to a third row, that implies a bunch of linear equations between the entries in those rows that fill in some of the entries if you know the others. – Qiaochu Yuan Jan 16 '18 at 23:32

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