Effect of embedding dimension on complexity measures in identifying Arrhythmia.

Entropy measures like Approximate entropy (ApEn) and Sample entropy (SampEn) are well established tools to analyze Heart Rate Variability (HRV) data. Critical parameters involved in these computations namely embedding dimension m and tolerance r are in most cases assumed to be 2 and 0.2*signal SD (standard devaition) respectively. Such assumptions do not work fairly across data sets and thus create misleading results in many cases. Problems with r have been addressed with the advent of newer entropy measures like Permutation entropy (PE), Fuzzy entropy (FuzzyEn) and Distribution entropy (DistEn) that simply eliminate, modify or replace r from calculations. On the other hand, the disadvantage of using a fixed assumed choice of m when such measures are used for data classification is yet to be investigated. The smallest variation in m may effect the extent of information retrieval from HRV data and hence it is extremely important to analyze different possibilities and outcomes of the same. In this study, we scrutinize the behavior of different entropy measures with regard to their classification performance at four different values of embedding dimension i.e., m = 2, 3,4 and 5. Normal and Arrhythmic RR intervals taken at data lengths ranging from 50 to 1000 have been used for the purpose. At any choice of m, DistEn and PE are the best measures to classify Arrhythmic data, whose AUC (Area under the ROC curve) values can go as high as 0.94 and 1 respectively. However PE performance becomes unstable with N for m > 3 (highest Δ being 0.3 at m = 5, Δ being the difference between minimum and maximum AUC). Irrespective of the choice of m, DistEn performance remains the most efficient and stable (highest Δ being only 0.03 at m = 4) for Arrhythmia classification. In the case of all other entropy measures, it is recommended that the value of m be chosen with discretion to ensure stability and efficiency in classification performance.