Fast-Parallel Singular Value Thresholding for Many Small Matrices based on Geometric Feature of Singular Values

This paper proposes a singular value thresholding (SVT) method called fast-parallel SVT for many small matrices that is based on the geometric feature of singular values. By discovering the geometric feature of singular values, SVT is expressed in a completely different format from conventional SVT methods. The new format does not require singular value decomposition, which is the calculation bottleneck with conventional SVT methods, so the amount of floating-point calculation can be reduced. The new format can also be described almost linearly, allowing many matrices to be processed in data in parallel. Through an experiment, the proposed method calculated SVT up to 162.84 times faster with higher calculation accuracy than conventional SVT methods.