Improving the performance of sample entropy in ultra-short-term time-series using kernel density estimation

As a widely used nonlinear dynamics metric, sample entropy (SampEn) quantifies the irregularity of time-series. We proposed a reliable approach for estimating SampEn in ultra-short-term time-series based on kernel density estimation, termed kernel sample entropy (kSampEn). kSampEn employs a kernel function to generate a smooth estimate of the cumulative distribution function (CDF) of inter-state distances, thereby alleviating the abrupt jumps observed in the empirical CDF used by conventional SampEn. Simulation results demonstrated that for time-series shorter than 30 data points, SampEn generally failed to produce valid estimates, whereas kSampEn remained robust under the tested conditions. Furthermore, SampEn frequently returned invalid estimates when applied to 30-second overnight RR interval segments, whereas kSampEn successfully quantified entropy and revealed higher entropy during non-rapid-eye-movement sleep compared with wakefulness or rapid-eye-movement sleep. In conclusion, kSampEn provides a reliable approach for analyzing cardiovascular signals in the context of sleep research and other applications involving short-term physiological time-series.