Nonlinear Kernel Dictionary Learning Algorithm Based on Analysis Sparse Model

In the past decades, relevant sparse representation models and their corresponding dictionary learning algorithms have been explored extensively as they could be applied in various fields. However, most of them are focusing the linear model and nonlinear one is still less touched, although there are plenty of nonlinear scenarios in real applications. To further address this kind of the unmet challenge, in this work we mainly focus the following two works (i) propose a kernel transformation based method directly transforming the nonlinear analysis problem into a linear one, which is exactly the standard sparse analysis form but implies all nonlinear information of the original problem; (ii) present a nonlinear dictionary learning algorithm by leveraging the kernel trick and the KSVD-like manner, which has its root in analysis sparse model rather than synthesis model. Then, the proposed methods are employed to address the classification problem. Benchmark experimental results on three well-known datasets show that the proposed algorithm in (ii) outperforms some related linear algorithms and other existing nonlinear dictionary learning algorithms. Moreover, when the data is interfered by noise or some pixels are missing in the data, the algorithm is also effective, which proves its theoretical advantages owing to analysis sparse model's merits of the equality of all atoms and the much smaller dimensionality for signal representation to some extent. And the classification accuracy of the proposed method in (i) is slightly lower than that of (ii), but better than that of other state of art methods.