Deep learned SVT: Unrolling singular value thresholding to obtain better MSE
This work addresses matrix completion tasks for applications like recommendation systems or signal processing, but it is incremental as it builds upon the existing SVT algorithm.
The authors tackled the affine rank minimization problem by proposing a trainable deep neural network called Learned SVT (LSVT), which unrolls the singular value thresholding (SVT) algorithm, resulting in lower mean squared error (MSE) and greater robustness compared to SVT with the same number of iterations.
Affine rank minimization problem is the generalized version of low rank matrix completion problem where linear combinations of the entries of a low rank matrix are observed and the matrix is estimated from these measurements. We propose a trainable deep neural network by unrolling a popular iterative algorithm called the singular value thresholding (SVT) algorithm to perform this generalized matrix completion which we call Learned SVT (LSVT). We show that our proposed LSVT with fixed layers (say T) reconstructs the matrix with lesser mean squared error (MSE) compared with that incurred by SVT with fixed (same T) number of iterations and our method is much more robust to the parameters which need to be carefully chosen in SVT algorithm.