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This repository contains code for Rotation-invariant gait identification with quaternion convolutional neural networks, arXiv 2020, by B Jing, V Prabhu, A Gu, and J Whaley.

Due to privacy considerations, we are not able to release the datasets or the training codes used to train the models described in the paper. This repository contains only the implementations of the QCNN kernels and model architecture, which should be sufficient to use QCNN in other domains of interest.

All quaternions should be represented as tensors of shape (4, 1), with the real part in the zeroth index. A tensor quaternion thought of as having shape dims, for example, should therefore actually have shape (*dims, 4, 1).

The implementation of the quaternion kernels are in qcnn.py. The main exports of interest are:

• qcnn.QConv1d Quaternion convolutional kernel, accepts arguments inchannels, outchannels, filterlen, stride=1 and tensors of shape (batch, in channels, in time, 4, 1).
• qcnn.QBatchNorm1d Quaternion batch norm, accepts arguments *dims, momentum=0.1 and tensors of shape (batch, *dims, time, 4, 1).
• qcnn.cuda() Call this once to prepare the kernel to run on GPU.

Some utility exports of interest are

• qcnn.checkGrad() Call this to check that the implementations of quaternion gradients are correct.
• qcnn.checkEquivariant() Call this to check that the quaternion kernel is equivariant.
• qcnn.qconj(q) Returns the conjugate of q.
• qcnn.qnormsq(q) Returns the squared norm of q.
• qcnn.qnorm(q) Returns the norm of q.
• qcnn.qinv(q) Returns the inverse of q.
• qcnn.rotate(q, r) Rotates quaternion q by rotation quaternion r.

Example usages can be found in models.py, which defines a CNN and QCNN in parallel to illustrate the similar usages of the nn.Conv1D, qcnn.QConv1d, nn.BatchNorm1D, and qcnn.QBatchNorm1d. These were also the models used for the multi-user experiments in the paper.