Geometric algebra based recurrent neural network for multi-dimensional time-series prediction - Li, Yanping; Wang, Yi; Wang, Yue; Qian, Chunhua; Wang, Rui (Frontiers in Computational Neuroscience, 2022)
Recurrent neural network (RNN) and its variants have achieved state-of-the-art performance in multi-dimensional time-series (MTS) prediction, which can serve as the basis for many practical applications. In addition to sequential characteristic, the different dimensions of MTS have strong internal dependencies. Recent RNN models deal with various dimensions of MTS as independent channels, which may lead to the loss of dependencies between different dimensions or the loss of associated information between each dimension and the global. This paper proposes a novel Long-and Short-term Time-series network based on geometric algebra (GA), dubbed GA-LSTNet, to process MTS in a holistic way without losing the inter-relationship among dimensions. Specifically, taking advantage of GA, multi-dimensional data at each time point of MTS is represented as GA multi-vectors to capture the inherent structures and preserve the correlation of those dimensions. In particular, traditional real-valued RNN, real-valued LSTM and the back-propagation through time are extended to the GA domain. We evaluate the performance of the proposed GA-LSTNet model in prediction tasks on four well-known MTS datasets. The experimental results indicate that our GA-LSTNet model outperforms traditional real-valued LSTNet with higher prediction accuracy.