Multivariate Multiscale Cosine Similarity Entropy and Its Application to Examine Circularity Properties in Division...

Area of Science:

• Complexity Science
• Signal Processing
• Nonlinear Dynamics

Background:

• Traditional univariate entropy methods like sample entropy (SampEn) and fuzzy entropy (FuzzyEn) measure signal irregularity.
• Multivariate extensions (MMSE, MMFE) analyze structural richness at high scales but face limitations with embedding dimensions and data size.
• Existing methods struggle with optimal scale range selection for varying signal characteristics.

Purpose of the Study:

• To introduce a novel multivariate entropy method, multivariate multiscale cosine similarity entropy (MMCSE), for quantifying structural complexity.
• To overcome the limitations of high-scale requirements in MMSE and MMFE.
• To enable analysis of signal self-correlation at low scales, relaxing constraints on embedding dimensions and data length.

Main Methods:

• Extension of the univariate cosine similarity entropy (CSE) to the multivariate domain, creating MMCSE.
• Quantification of structural complexity based on the degree of self-correlation within signals.
• Application of MMCSE to analyze complex and quaternion circularity properties of signals with diverse correlation behaviors.

Main Results:

• MMCSE effectively quantifies structural complexity by measuring signal self-correlation at low scales.
• The proposed method relaxes prohibitive constraints between embedding dimension and data length, improving flexibility.
• Simulations demonstrate that MMCSE outperforms standard methods (MMSE, MMFE) in analyzing signals with varying correlation properties.

Conclusions:

• MMCSE offers a robust and flexible alternative for analyzing multivariate signal complexity, particularly at low scales.
• The method's ability to assess self-correlation provides new insights into signal structure and dynamics.
• MMCSE represents a significant advancement over existing multivariate entropy methods for complex signal analysis.