Cv-CapsNet: Complex-valued capsule network

Abstract

Capsule network (CapsNet) can recognize the objects by encoding the part-whole relationships in a way similar to our human perceptual system and has already shown its great potential in image classification tasks. However, it is limited to the real domain while the complex numbers having much richer representational capacity and facilitating the noise-robust memory retrieval mechanisms. Therefore, we propose two architectures: Complex-valued Dense CapsNet (Cv-CapsNet) and Complex-valued Diverse CapsNet (Cv-CapsNet++), each of them consists of three stages. In the first stage, multi-scale complex-valued features are obtained by the restricted dense complex-valued subnetwork. Particularly, Cv-CapsNet++ utilizes a three-level Cv-CapsNet hierarchical model to extract the multi-scale high-level complex-valued features in order to adapt to the complicated datasets. In the second stage, these complex-valued features are encoded into the complex-valued primary capsules, Particularly, Cv-CapsNet++ encodes the complex-valued features from different hierarchies into the multi-dimensional complex-valued primary capsules. In the third stage, we generalize the dynamic routing algorithm to the complex-valued domain and employ it to fuse the real- and imaginary-valued information of complex-valued primary capsules. The experimental results show that the proposed architectures lead to fewer trainable parameters, better performance, and fewer iterations during training than Real-valued CapsNets (Rv-CapsNets) with similar structure and original CapsNet on FashionMNIST and CIFAR10 datasets.