A characteristic ridge-ledge in entropy surfaces of cardiovascular time series estimated by the Norm Component Matrix algorithm

Sample entropy (SampEn) is a popular complexity measure in HRV analysis. SampEn is estimated by fixing the values of the embedding dimension "m" and distance threshold "r" and traditionally SampEn is calculated with m=2 and r=0.2 times the standard deviation of the series. Attempts to extend the estimates to different (m, r) pairs are hampered by the high computational burden of the traditional algorithm. We recently proposed an extremely fast Norm Component Matrix (NCM) algorithm for SampEn calculation which allows analyzing whole ranges of (m, r) values leading to entropy surfaces. This paper is the first attempt to calculate these surfaces by NCM and to describe their properties for both synthetic and physiological time series. We show that the entropy surface has a characteristic ridge-ledge structure associated with the randomness in the data.