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 high-lighted the need for the analysis of nonlinear dynamical properties at a higher level - the so-called structural complexity. Traditional single-scale entropy measures, such as the amplitude based Sample Entropy (SampEn), are designed to give a quantification of irregularity and 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 at a cost of the reduction of the number of sample points that results in reduced stability and limitations regarding the selection 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 within a system at both a low and large scales, and thus assess the true structural complexity in a more physically meaningful way. Both synthetic and real world signals are utilized to examine the performance of the proposed approach, with the resulting simulations supporting the approach.