Randomized non-linear PCA networks

PCANet is an unsupervised Convolutional Neural Network (CNN), which uses Principal Component Analysis (PCA) to learn convolutional filters. One drawback of PCANet is that linear PCA cannot capture nonlinear structures within data. To address this problem, a straightforward approach is utilizing kernel methods by equipping the PCA method in PCANet with a kernel function. However, this practice leads to a network having cubic complexity with respect to the number of training image patches. In this paper, we propose a network called Randomized Nonlinear PCANet (RNPCANet), which uses an explicit kernel PCA to learn the convolutional filters. Although RNPCANet utilizes kernel methods for nonlinear processing of data, using kernel approximation techniques to define an explicit feature space in each stage, we theoretically show that the complexity of this model is not much higher than that of PCANet. We also show that our method links PCANets to Convolutional Kernel Networks (CKNs) as the proposed model maps the patches to a kernel feature space similar to CKNs. We evaluate our model on image recognition tasks including Coil-20, Coil-100, ETH-80, Caltech-101, MNIST, and C-Cube datasets. The experimental results show that the proposed method has superiority over PCANet and CKNs in terms of recognition accuracy.