Generalized relational tensors for chaotic time series.

Area of Science:

• Data Science
• Time Series Analysis
• Computational Intelligence

Background:

• Time series data analysis is crucial across various scientific domains.
• Existing methods for storing and predicting time series data have limitations, especially for complex or chaotic datasets.

Purpose of the Study:

• To introduce a novel discrete structure, the generalized relational tensor, for effective time series information storage.
• To develop and evaluate algorithms for filling, regenerating, and predicting time series using this structure.
• To assess the performance of these algorithms, particularly for chaotic time series.

Main Methods:

• Development of algorithms integrating generalized z-vectors with ant colony optimization techniques.
• Utilizing a difference metric between initial and regenerated time series characteristics to evaluate data storage and regeneration quality.
• Employing metrics like the largest Lyapunov exponent and auto-correlation function for chaotic time series analysis.

Main Results:

• The generalized relational tensor and associated algorithms demonstrate effective time series storage and regeneration.
• Fairly good results were achieved for periodic and benchmark chaotic time series.
• Satisfactory performance was observed for real-world chaotic time series data.

Conclusions:

• The proposed generalized relational tensor offers a viable discrete structure for time series data.
• The developed algorithms show effectiveness in storing, regenerating, and predicting time series, including chaotic ones.
• The approach provides a valuable tool for analyzing complex time series data in scientific research.