  Capsule networks use routing algorithms to flow information between
consecutive layers. In the existing routing procedures, capsules produce
predictions (termed votes) for capsules of the next layer. In a nutshell, the
next-layer capsule's input is a weighted sum over all the votes it receives. In
this paper, we propose non-iterative cluster routing for capsule networks. In
the proposed cluster routing, capsules produce vote clusters instead of
individual votes for next-layer capsules, and each vote cluster sends its
centroid to a next-layer capsule. Generally speaking, the next-layer capsule's
input is a weighted sum over the centroid of each vote cluster it receives. The
centroid that comes from a cluster with a smaller variance is assigned a larger
weight in the weighted sum process. Compared with the state-of-the-art capsule
networks, the proposed capsule networks achieve the best accuracy on the
Fashion-MNIST and SVHN datasets with fewer parameters, and achieve the best
accuracy on the smallNORB and CIFAR-10 datasets with a moderate number of
parameters. The proposed capsule networks also produce capsules with
disentangled representation and generalize well to images captured at novel
viewpoints. The proposed capsule networks also preserve 2D spatial information
of an input image in the capsule channels: if the capsule channels are rotated,
the object reconstructed from these channels will be rotated by the same
transformation. Codes are available at
https://github.com/ZHAOZHIHAO/ClusterRouting.
