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：本文提出一种新颖的四元数时间序列压缩方法：将长时序列分为数据段，提取各数据段的最小值、最大值、均值与标准差作为代表性特征，并将其封装为四元数，从而获得四元数值时间序列。该序列经四元数神经网络层处理，通过哈密顿乘积保持特征间关联。为训练此四元数神经网络，我们采用GHR微积分推导四元数反向传播算法，该算法是四元数空间中有效乘积运算与链式法则的必要前提。进一步研究了所推导更新规则与自动微分之间的关联。在田纳西伊士曼数据集上应用所提压缩方法，并在两种设置下利用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。两种场景中，本方法均优于实数值对应模型及两种基线模型（输入为未压缩原始时间序列的模型、采用均值规则降采样的模型）。此外，将SimCLR-TS设定的分类基准从81.43%提升至83.90%。