SO(2) equivariant and invariant representation learning using graph convolutional network

Abstract

Training a Convolutional Neural Network (CNN) to be robust against rotation has mostly been done with data augmentation. In this thesis, another progressive vision of research direction is highlighted to encourage less dependence on data augmentation by achieving structural rotational invariance of a network. The deep SO(2) equivariant and invariant network is proposed, which consists of two main parts, to echo such vision. First, Self-Weighted Nearest Neighbors Graph Convolutional Network (SWN-GCN) is proposed to implement Graph Convolutional Network (GCN) on the graph representation of an image to acquire rotationally equivariant representation, as GCN is more suitable for constructing deeper network than spectral graph convolution-based approaches. Then, invariant representation is eventually obtained with Global Average Pooling (GAP), a permutation-invariant operation suitable for aggregating high-dimensional representations, over the equivariant set of vertices retrieved from SWN-GCN. Our method achieves the state-of-the-art image classification performance on rotated MNIST and CIFAR-10 images, where the models are trained with a non-augmented dataset only. Then, quantitative and qualitative validations over invariance and equivariance of the representations are reported, respectively. Part of this work was presented at British Machine Vision Conference (BMVC) in 2021.