Robust dictionary learning with capped ℓ₁-Norm

Expressing data vectors as sparse linear combinations of basis elements (dictionary) is widely used in machine learning, signal processing, and statistics. It has been found that dictionaries learned from data are more effective than off-the-shelf ones. Dictionary learning has become an important tool for computer vision. Traditional dictionary learning methods use quadratic loss function which is known sensitive to outliers. Hence they could not learn the good dictionaries when outliers exist. In this paper, aiming at learning dictionaries resistant to outliers, we proposed capped ℓ₁-norm based dictionary learning and an efficient iterative re-weighted algorithm to solve the problem. We provided theoretical analysis and carried out extensive experiments on real word datasets and synthetic datasets to show the effectiveness of our method.