I want to know if is it possible to get a derivative or an approximation of the derivative of the trace norm with respect to a column. More specifically if we have a matrix containing in each of its elements a function of a parameter 'w', how to get the derivative of the trace norm of this matrix with respect to 'w'?
Trace norm differentiation with respect to a column
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optimization
convex-optimization
machine-learning
matrix-rank
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0Well, how would you use the chain rule in this context? I know that the derivative of the trace norm with respect to the concerned matrix is UV' where U and V come from the svd decomposition (supposing that the singular values are all positives) but i want something different. I want the derivative with respect to a parameter present in the elements of the matrix. – 2017-02-23
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0What's the dependence of the matrix elements on the parameter? Can you apply the chain rule? – 2017-02-23
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0That doesn't make much sense to me. You mind want to expand your question with more details of your work. – 2017-02-23