MULTIVARIATE MULTISCALE COSINE SIMILARITY ENTROPY

The rapid development in sensor technology has made it convenient to acquire data from multi-channel systems but has also highlighted the need for the analysis of dynamical properties - the so-called structural complexity. Traditional single-scale entropy measures, such as the Sample Entropy (SampEn), are designed to give a quantification of randomness. Its enhanced versions, Multiscale Sample Entropy (MSampEn) and Multivariate Multiscale Sample Entropy (MMSE), are capable of detecting the structure within a signal at high scales and for multivariate data, however, the scaling process comes with a shortage of sample points that results in reduced stability and limitated selections of the embedding dimension. In addition, the analyses of structure on the basis of MSampEn and MMSE require relatively high scales, yet without prior-knowledge of the scale degree. To this end, we propose a new multivariate entropy method based on the recently introduced Cosine Similarity Entropy (CSE). The proposed Multivariate Multiscale Cosine Similarity Entropy (MMCSE) is based on angular distance which makes it possible to assess long-term correlation of the system at both a low and large scale. Both synthetic and real world signals are utilized to examine the performance of the proposed approach, with the resulting simulations supporting the approach.