“Low-rank + dual” model based dimensionality reduction

We propose a novel “low-rank + dual” model for the matrix decomposition problems. Based on the unitarily invariant property of the Schatten p  -norm, we prove that the solution of the proposed model can be obtained by an “l∞+l1l∞+l1” minimization problem, thus a simple and fast algorithm can be provided to solve our new model. Furthermore, we find that applying “l∞+l1l∞+l1” to any vector can achieve a shifty threshold on the values. Experiments on the simulation data, the real surveillance video database and the Yale B database prove the proposed method to outperform the state-of-the-art techniques.