We propose a novel quaternionic time-series compression methodology where we divide a long time-series into segments of data, extract the min, max, mean and standard deviation of these chunks as representative features and encapsulate them in a quaternion, yielding a quaternion valued time-series. This time-series is processed using quaternion valued neural network layers, where we aim to preserve the relation between these features through the usage of the Hamilton product. To train this quaternion neural network, we derive quaternion backpropagation employing the GHR calculus, which is required for a valid product and chain rule in quaternion space. Furthermore, we investigate the connection between the derived update rules and automatic differentiation. We apply our proposed compression method on the Tennessee Eastman Dataset, where we perform fault classification using the compressed data in two settings: a fully supervised one and in a semi supervised, contrastive learning setting. Both times, we were able to outperform real valued counterparts as well as two baseline models: one with the uncompressed time-series as the input and the other with a regular downsampling using the mean. Further, we could improve the classification benchmark set by SimCLR-TS from 81.43% to 83.90%.

翻译：我们提出了一种新颖的四元数时间序列压缩方法：将长时序列划分为数据段，提取每个分段的极小值、极大值、均值与标准差作为代表性特征，并将其封装为四元数，从而构建四元数值时间序列。该时间序列通过四元数神经网络层进行处理，旨在利用哈密顿乘积保持特征间的关联。为训练此四元数神经网络，我们基于GHR微积分推导了四元数反向传播算法——该微积分为四元数空间中有效的乘积与链式法则所必需。此外，我们探究了推导的更新规则与自动微分之间的内在联系。将所提压缩方法应用于田纳西-伊斯曼数据集，我们在两种场景下基于压缩数据进行故障分类：全监督设置与半监督对比学习设置。两种场景下，我们的方法均优于实值对应模型及两个基线模型：一个以未压缩时间序列作为输入，另一个采用基于均值的常规降采样方法。此外，我们将SimCLR-TS的分类基准从81.43%提升至83.90%。