# Time Series Compression using Quaternion Valued Neural Networks and Quaternion Backpropagation

arXiv: https://arxiv.org/abs/2403.11722 · HTML: https://mlsanity.com/paper/2403.11722/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 81 references that are in the map.
- First posted on arXiv 18 Mar 2024.

## Builds on (most cited first, 18 of 18)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [Deep Complex Networks](https://mlsanity.com/paper/1705.09792/) (2017)
- [Deep Quaternion Networks](https://mlsanity.com/paper/1712.04604/) (2017)
- [Quaternion Convolutional Neural Networks](https://mlsanity.com/paper/1903.00658/) (2019)
- [Quaternion Recurrent Neural Networks](https://mlsanity.com/paper/1806.04418/) (2018)
- [3D-Rotation-Equivariant Quaternion Neural Networks](https://mlsanity.com/paper/1911.09040/) (2019)
- [Quaternion Convolutional Neural Networks for Heterogeneous Image Processing](https://mlsanity.com/paper/1811.02656/) (2018)
- [Quaternion Generative Adversarial Networks](https://mlsanity.com/paper/2104.09630/) (2021)
- [A Quaternion-Valued Variational Autoencoder](https://mlsanity.com/paper/2010.11647/) (2020)
- [Speech Emotion Recognition Using Quaternion Convolutional Neural Networks](https://mlsanity.com/paper/2111.00404/) (2021)
- [Quaternion Gradient and Hessian](https://mlsanity.com/paper/1406.3587/) (2014)
- [Speech recognition with quaternion neural networks](https://mlsanity.com/paper/1811.09678/) (2018)
- [Predicting Rigid Body Dynamics using Dual Quaternion Recurrent Neural Networks with Quaternion Attention](https://mlsanity.com/paper/2011.08734/) (2020)
- [Understanding Vector-Valued Neural Networks and Their Relationship with Real and Hypercomplex-Valued Neural Networks](https://mlsanity.com/paper/2309.07716/) (2023)
- [LFZip: Lossy compression of multivariate floating-point time series data via improved prediction](https://mlsanity.com/paper/1911.00208/) (2019)

## Built on by (most cited first, 3 of 3)

- [Improving Quaternion Neural Networks with Quaternionic Activation Functions](https://mlsanity.com/paper/2406.16481/) (2024)
- [Asymptotically Stable Quaternion-valued Hopfield-structured Neural Network with Periodic Projection-based Supervised Learning Rules](https://mlsanity.com/paper/2510.16607/) (2025)
- [EdgeLDR: Quaternion Low-Displacement Rank Neural Networks for Edge-Efficient Deep Learning](https://mlsanity.com/paper/2601.05379/) (2026)

## Abstract (arXiv)

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%.