Geometric algebra based recurrent neural network for multi-dimensional time-series prediction.

Area of Science:

• Machine Learning
• Time Series Analysis
• Geometric Algebra

Background:

• Current recurrent neural network (RNN) models often treat multivariate time-series (MTS) dimensions independently, risking loss of crucial inter-dimensional dependencies and global correlations.
• Existing methods struggle to capture the holistic nature of MTS data, leading to suboptimal prediction performance.

Purpose of the Study:

• To propose a novel Long-and Short-term Time-series network based on geometric algebra (GA), named GA-LSTNet, for improved MTS prediction.
• To leverage geometric algebra for a more comprehensive representation of MTS data, preserving inherent structures and correlations between dimensions.

Main Methods:

• Representing multi-dimensional data at each time point of MTS as GA multi-vectors.
• Extending traditional real-valued RNN, LSTM, and back-propagation through time to the GA domain.
• Developing the GA-LSTNet architecture to process MTS data holistically.

Main Results:

• GA-LSTNet demonstrated superior prediction performance compared to six other methods on four well-known MTS datasets.
• The proposed model achieved higher prediction accuracy than the traditional real-valued LSTNet.
• The GA-based approach effectively captures and preserves inter-dimensional relationships in MTS data.

Conclusions:

• GA-LSTNet offers a more accurate and holistic approach to MTS prediction by utilizing geometric algebra.
• The findings suggest that geometric algebra provides a powerful framework for enhancing time-series analysis models.
• This novel method addresses existing shortcomings in MTS prediction models, paving the way for more robust solutions.