Singular Value Decomposition Entropy for Complex Data Analysis.

Area of Science:

• Complex Systems Analysis
• Information Theory
• Data Science

Background:

• Entropy-based methods are crucial for analyzing complex systems, characterizing fractality, time reversibility, and nonlinearity.
• Traditional methods often struggle to capture intricate patterns, necessitating advanced analytical techniques.
• Shannon entropy is useful but limited for short data; approximate, sample, and permutation entropies have parameter-dependence issues.

Purpose of the Study:

• To review recent applications of Singular Value Decomposition (SVD) entropy across diverse scientific fields.
• To explore the potential of SVD entropy in detecting nonlinearity within complex datasets.
• To investigate the utility of SVD entropy in transfer entropy analysis for time series.

Main Methods:

• Utilizing Singular Value Decomposition (SVD) entropy as a framework for assessing pattern diversity and dataset dimensionality.
• Comparing SVD entropy with other entropy-based methods like Shannon, approximate, sample, and permutation entropies.
• Analyzing time series data to evaluate nonlinearity detection and transfer entropy capabilities.

Main Results:

• SVD entropy provides a valuable index for pattern diversity and approximate dimensionality.
• Recent studies demonstrate SVD entropy's effectiveness in various application domains.
• The method shows promise for enhancing nonlinearity detection and time series analysis.

Conclusions:

• SVD entropy presents a flexible and powerful tool for complex data analysis, particularly for pattern diversity and dimensionality assessment.
• Its application extends to advanced analyses like nonlinearity detection and transfer entropy, offering advantages over traditional methods.
• Further exploration of SVD entropy in diverse fields is warranted to fully leverage its capabilities.