Cuesta-Frau David, Kouka Mahdy, Silvestre-Blanes Javier, Sempere-Payá Víctor
Technological Institute of Informatics (ITI), Universitat Politècnica de València, Alcoi Campus, 03801 Alcoi, Spain.
Department of System Informatics and Computers, Universitat Politècnica de València, 46022 Valencia, Spain.
Entropy (Basel). 2022 Dec 30;25(1):66. doi: 10.3390/e25010066.
Slope Entropy (SlpEn) is a very recently proposed entropy calculation method. It is based on the differences between consecutive values in a time series and two new input thresholds to assign a symbol to each resulting difference interval. As the histogram normalisation value, SlpEn uses the actual number of unique patterns found instead of the theoretically expected value. This maximises the information captured by the method but, as a consequence, SlpEn results do not usually fall within the classical [0,1] interval. Although this interval is not necessary at all for time series classification purposes, it is a convenient and common reference framework when entropy analyses take place. This paper describes a method to keep SlpEn results within this interval, and improves the interpretability and comparability of this measure in a similar way as for other methods. It is based on a max-min normalisation scheme, described in two steps. First, an analytic normalisation is proposed using known but very conservative bounds. Afterwards, these bounds are refined using heuristics about the behaviour of the number of patterns found in deterministic and random time series. The results confirm the suitability of the approach proposed, using a mixture of the two methods.
斜率熵（SlpEn）是一种最近才提出的熵计算方法。它基于时间序列中连续值之间的差异以及两个新的输入阈值，以便为每个所得的差异区间分配一个符号。作为直方图归一化值，SlpEn使用实际发现的独特模式数量，而不是理论预期值。这使得该方法捕获的信息最大化，但结果是，SlpEn的结果通常不在经典的[0,1]区间内。尽管对于时间序列分类目的而言，这个区间并非完全必要，但在进行熵分析时，它是一个方便且通用的参考框架。本文描述了一种使SlpEn结果保持在该区间内的方法，并以与其他方法类似的方式提高了该度量的可解释性和可比性。它基于一种最大 - 最小归一化方案，分两步描述。首先，使用已知但非常保守的界限提出一种解析归一化方法。之后，利用关于确定性和随机时间序列中发现的模式数量行为的启发式方法对这些界限进行细化。结果证实了所提出方法的适用性，该方法结合了这两种方法。
