Publication: Multivariate Multiscale Cosine Similarity Entropy and Its Application to Examine Circularity Properties in Division Algebras †
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Issued Date
2022
Resource Type
Language
eng
File Type
application/pdf
ISSN
10994300
Rights Holder(s)
Scopus
Bibliographic Citation
Journal of Aquatic Animal Health. Vol , No. (2022), p.-
Suggested Citation
Xiao H., Chanwimalueang T., Mandic D.P. Multivariate Multiscale Cosine Similarity Entropy and Its Application to Examine Circularity Properties in Division Algebras †. Journal of Aquatic Animal Health. Vol , No. (2022), p.-. doi:10.3390/e24091287 Retrieved from: https://hdl.handle.net/20.500.14740/9633
Author(s)
Abstract
The extension of sample entropy methodologies to multivariate signals has received considerable attention, with traditional univariate entropy methods, such as sample entropy (SampEn) and fuzzy entropy (FuzzyEn), introduced to measure the complexity of chaotic systems in terms of irregularity and randomness. The corresponding multivariate methods, multivariate multiscale sample entropy (MMSE) and multivariate multiscale fuzzy entropy (MMFE), were developed to explore the structural richness within signals at high scales. However, the requirement of high scale limits the selection of embedding dimension and thus, the performance is unavoidably restricted by the trade-off between the data size and the required high scale. More importantly, the scale of interest in different situations is varying, yet little is known about the optimal setting of the scale range in MMSE and MMFE. To this end, we extend the univariate cosine similarity entropy (CSE) method to the multivariate case, and show that the resulting multivariate multiscale cosine similarity entropy (MMCSE) is capable of quantifying structural complexity through the degree of self-correlation within signals. The proposed approach relaxes the prohibitive constraints between the embedding dimension and data length, and aims to quantify the structural complexity based on the degree of self-correlation at low scales. The proposed MMCSE is applied to the examination of the complex and quaternion circularity properties of signals with varying correlation behaviors, and simulations show the MMCSE outperforming the standard methods, MMSE and MMFE. © 2022 by the authors.