Discriminative Nonlinear Analysis Operator Learning: When Cosparse Model Meets Image Classification

A linear synthesis model-based dictionary learning framework has achieved remarkable performances in image classification in the last decade. Behaved as a generative feature model, it, however, suffers from some intrinsic deficiencies. In this paper, we propose a novel parametric nonlinear analysis cosparse model (NACM) with which a unique feature vector will be much more efficiently extracted. Additionally, we derive a deep insight to demonstrate that NACM is capable of simultaneously learning the task-adapted feature transformation and regularization to encode our preferences, domain prior knowledge, and task-oriented supervised information into the features. The proposed NACM is devoted to the classification task as a discriminative feature model and yield a novel discriminative nonlinear analysis operator learning framework (DNAOL). The theoretical analysis and experimental performances clearly demonstrate that DNAOL will not only achieve the better or at least competitive classification accuracies than the state-of-the-art algorithms, but it can also dramatically reduce the time complexities in both training and testing phases.