dm.cs.tu-dortmund.de/mlbits/matrix-factorization-svd/
SVD as Matrix Factorization – Lecture Notes
\(k\) :
\[\min _{U_k,\Sigma _k,V_k} \left\lVert \smash {A - U_k\Sigma _kV_k^T}\mathstrut \right\rVert ^2\]
where \(U_k\) , \(\Sigma _k\) , \(V_k\) are the matrixes \(U\) , \(\Sigma\) , \(V\) truncated to \(k\) [...] A_{k-1} + u_k \sigma_k v_k^T\]
and the residuals
\[\left\lVert \smash {A-A_k}\mathstrut \right\rVert ^2 = \sum \nolimits _{i=k+1}^n \sigma_i\]
➜ SVD gives us least-squares best approximations of rank \(k=1\ldots …
