Online multiscale entropy estimation using distribution statistics

Multiscale entropy (MSE) is a measurement for quantifying the randomness of a sequence of data. Recently, it has been proven to be the most effective way to analyze the complexity of physiological signals in biomedicine and other fields. The implementation of MSE is computationally expensive because it considers multiple complexities of several data sequences with multiple scales and the computation of entropy for each data sequence is time consuming. A large number of original observed data for computing MSE is necessary because the number of data reduces when the scale increases. We must confirm that the data for each scale is enough to robustly obtain entropy. The large data problem makes MSE difficult for online application of processing sequential data. This paper provides a new online MSE computation method to improve computation efficiency of MSE. Furthermore, we apply distribution statistics in online MSE computation procedure to reduce the storage space of a system. In addition to segmenting the original data sequence into several non-overlapped sliding windows to reduce the data amount of each computation, different kinds of metadata are defined for metadata updating algorithm to accelerate computation time and save storage space. Experiments analyses with electrocardiogram (ECG) revealed that the proposed MSE estimation methods achieved significant improvement of more than 15 times faster than the conventional method for N= 60,000. Moreover, the proposed method only uses about 1/500,000 storage space compared to the conventional method.