Slope Entropy Characterisation: The Role of the δ Parameter

Many time series entropy calculation methods have been proposed in the last few years. They are mainly used as numerical features for signal classification in any scientific field where data series are involved. We recently proposed a new method, Slope Entropy (SlpEn), based on the relative frequency of differences between consecutive samples of a time series, thresholded using two input parameters, γ and δ. In principle, δ was proposed to account for differences in the vicinity of the 0 region (namely, ties) and, therefore, was usually set at small values such as 0.001. However, there is no study that really quantifies the role of this parameter using this default or other configurations, despite the good SlpEn results so far. The present paper addresses this issue, removing δ from the SlpEn calculation to assess its real influence on classification performance, or optimising its value by means of a grid search in order to find out if other values beyond the 0.001 value provide significant time series classification accuracy gains. Although the inclusion of this parameter does improve classification accuracy according to experimental results, gains of 5% at most probably do not support the additional effort required. Therefore, SlpEn simplification could be seen as a real alternative.