Optimal Selection of Threshold Value 'r' for Refined Multiscale Entropy

Refined multiscale entropy (RMSE) technique was introduced to evaluate complexity of a time series over multiple scale factors 't'. Here threshold value 'r' is updated as 0.15 times SD of filtered scaled time series. The use of fixed threshold value 'r' in RMSE sometimes assigns very close resembling entropy values to certain time series at certain temporal scale factors and is unable to distinguish different time series optimally. The present study aims to evaluate RMSE technique by varying threshold value 'r' from 0.05 to 0.25 times SD of filtered scaled time series and finding optimal 'r' values for each scale factor at which different time series can be distinguished more effectively. The proposed RMSE was used to evaluate over HRV time series of normal sinus rhythm subjects, patients suffering from sudden cardiac death, congestive heart failure, healthy adult male, healthy adult female and mid-aged female groups as well as over synthetic simulated database for different datalengths 'N' of 3000, 3500 and 4000. The proposed RMSE results in improved discrimination among different time series. To enhance the computational capability, empirical mathematical equations have been formulated for optimal selection of threshold values 'r' as a function of SD of filtered scaled time series and datalength 'N' for each scale factor 't'.