Online Adaptive Kernel Learning with Random Features for Large-scale Nonlinear Classification.

• A novel random feature map is provided to improve the flexibility of kernel function, which can make the training samples linearly or approximately linear separable in high dimensional feature space. • Random features based online adaptive kernel learning is proposed to deal with large-scale nonlinear classification, which guarantees the learning model can better adapt to the change of data distribution shape when data is coming one by one. • The experiment results are conducted on twelve data sets and the results show that the proposed algorithm outperforms the state-of-the-art online methods on most data sets. Besides, the test accuracy of RF-OAK is comparable with that of offline deep learning algorithm on most data sets. In the field of support vector machines, online random feature map algorithms are very important methods for large-scale nonlinear classification problems. At present, the existing methods have the following shortcomings: (1) If only the hyperplane vector is updated during learning while the random feature components are fixed, there is no guarantee that these online methods can adapt to the change of data distribution shape when the data is coming one by one. (2) When the kernel is selected improperly, the samples mapped to an inappropriate space may not be well classified. In order to overcome these shortcomings, considering the fact that iteratively updating random feature components can make data better fit in the current space and lead to the flexible adjustment of the kernel function, random features based online adaptive kernel learning (RF-OAK) is proposed for large-scale nonlinear classification problems. Theoretical analysis of the proposed algorithm is also provided. The experimental results and the Wilcoxon signed-ranks test show that in terms of test accuracy, the proposed method is significantly better than the state-of-the-art online feature mapping classification methods. Compared with the deep learning algorithms, the training time of RF-OAK is shorter. In terms of test accuracy, RF-OAK is better than online algorithm and comparable with offline algorithms. [ABSTRACT FROM AUTHOR]