  A desireable property of accelerometric gait-based identification systems is
robustness to new device orientations presented by users during testing but
unseen during the training phase. However, traditional Convolutional neural
networks (CNNs) used in these systems compensate poorly for such
transformations. In this paper, we target this problem by introducing
Quaternion CNN, a network architecture which is intrinsically layer-wise
equivariant and globally invariant under 3D rotations of an array of input
vectors. We show empirically that this network indeed significantly outperforms
a traditional CNN in a multi-user rotation-invariant gait classification
setting .Lastly, we demonstrate how the kernels learned by this QCNN can also
be visualized as basis-independent but origin- and chirality-dependent
trajectory fragments in the euclidean space, thus yielding a novel mode of
feature visualization and extraction.
