Time series compression using quaternion valued neural networks and quaternion backpropagation

Area of Science:

• Data Science
• Machine Learning
• Signal Processing

Background:

• Time series data often requires efficient compression for analysis.
• Existing methods may not fully capture complex inter-feature relationships.
• Quaternions offer a framework for representing multi-component data.

Purpose of the Study:

• To develop a novel quaternionic time series compression methodology.
• To apply this method for fault classification using quaternion-valued neural networks.
• To compare the performance against real-valued and baseline models.

Main Methods:

• Segmenting time series and extracting statistical features (min, max, mean, std dev).
• Encapsulating features into quaternion values to create a quaternion-valued time series.
• Utilizing quaternion-valued neural networks with quaternion backpropagation (GHR calculus).
• Applying the method to the Tennessee Eastman Dataset for fault classification.

Main Results:

• The proposed quaternionic compression method outperformed real-valued counterparts.
• Achieved superior results in both fully supervised and semi-supervised contrastive learning settings.
• Improved the fault classification benchmark accuracy from 81.43% to 83.90%.

Conclusions:

• Quaternionic time series compression is effective for fault classification tasks.
• The method preserves feature relationships via the Hamilton product.
• Quaternion-valued neural networks trained with derived backpropagation show promise.