| Abstract: | The conversion functions in the hidden layer of radial basis function neural networks (RBFNN) are Gaussian functions. The Gaussian functions are local to the kernel centers. In most of the existing research, the spatial local response of the sample is inaccurately calculated because the kernels have the same shape as a hypersphere, and the kernel parameters in the network are determined by experience. The influence of the fine structure in the local space is not considered during feature extraction. In addition, it is difficult to obtain a better feature extraction ability with less computational complexity. Therefore, this paper develops a multi-scale RBF kernel learning algorithm and proposes a new multi-layer RBF neural network model. For the samples of each class, the expectation maximization (EM) algorithm is used to obtain multi-layer nested sub-distribution models with different local response ranges, which are called multi-scale kernels in the network. The prior information of each sub-distribution is used as the connection weight between the multi-scale kernels. Finally, feature extraction is implemented using multi-layer kernel subspace embedding. The multi-scale kernel learning model can efficiently and accurately describe the fine structure of the samples and is fault tolerant to setting the number of kernels to a certain extent. Considering the prior probability of each kernel as the weight makes the feature extraction process satisfy the Bayes rule, which can enhance the interpretability of feature extraction in the network. This paper also theoretically proves that the proposed neural network is a generalized version of the original RBFNN. The experimental results show that the proposed method has better performance compared with some state-of-the-art algorithms. |
