Robust two-dimensional PCANet with F-norm distance metric

Abstract

The principal component analysis network (PCANet) is a simplified convolutional neural network (CNN) implemented using a deep subspace learning model. Since its typical PCA filters utilize the squared Frobenius-norm (F-norm) as the distance metric, it exhibits extreme sensitivity to outliers hidden within the data. Furthermore, PCANet faces challenges in extracting structural information in the row and column directions of images as the filters need to be pre-vectorized. To address these issues, we propose a robust bi-directional two-dimensional PCANet (RBDPCANet), wherein the filters utilize the F-norm instead of the squared F-norm to mitigate the impact of outliers. Additionally, the relationship between reconstruction errors and projection distances is simultaneously considered in the objective function. After a concise analytical description of the PCANet concept and related work, we present the methodology for generating three convolutional kernels in the form of RBDPCANet-1, RBDPCANet-2, and RBDPCANet-3 algorithms. These convolution kernels are iteratively obtained and are suitable for numerical implementation. Each of the three algorithms uses another optimization objective function. It has been shown that in image recognition tasks, the developed methods are characterized by better resistance to noise compared to the classic PCANet approach. The rotation invariance and convergence of RBDPCANet are demonstrated according to theoretical principles. The efficacy of the proposed method is validated using images from publicly available datasets. Extensive experimental results on these datasets demonstrate that the proposed RBDPCANet not only significantly boosts the efficiency of image classification but also has strong resistance to occlusions, changes in lighting, changes in orientation, etc. Our implementation code is available at https://github.com/Wesley-li1/RBDPCANet-.