Minimal Shrinkage for Noisy Data Recovery Using Schatten-p Norm Objective

Noisy data recovery is an important problem in machine learning field, which has widely applications for collaborative prediction, recommendation systems, etc. One popular model is to use trace norm model for noisy data recovery. However, it is ignored that the reconstructed data could be shrank (i.e., singular values could be greatly suppressed). In this paper, we present novel noisy data recovery models, which replaces the standard rank constraint (i.e., trace norm) using Schatten-p Norm. The proposed model is attractive due to its suppression on the shrinkage of singular values at smaller parameter p. We analyze the optimal solution of proposed models, and characterize the rank of optimal solution. Efficient algorithms are presented, the convergences of which are rigorously proved. Extensive experiment results on 6 noisy datasets demonstrate the good performance of proposed minimum shrinkage models.