基于分数微分的时间序列相似性度量及其应用

时间序列的相似性度量是时间序列聚类、分类以及其他相关时间序列分析的基础.传统基于距离的相似性度量方法，忽视了时间序列可能存在的时间上的联系，而将时间序列看作一系列孤立点的集合.对于序列间可能存在的前后联系，基于分数阶微分的遗传特性和记忆特性，提出一种新的时间序列聚类的相似性度量.根据时间序列的分数阶微分计算新序列间的点距离，将其作为聚类算法的输入对时间序列进行聚类.仿真实验结果表明，与基于原始序列矢量距离的聚类结果相比，新的分数阶相似性度量方法表现更好.

Time series similarity measurement based on fractionaldifferential and its application

Similarity measures of time series are the basis for time series clustering, classification and other related time series analysis. The traditional distance-based similarity measure ignores the possible temporal connections of time series and treats time series as a series of isolated point sets. For the possible backward and forward connections between sequences, a new similarity measure for time series clustering is proposed based on the genetic and memory properties of fractional order differentiation. The point distances between the new sequences are calculated based on the fractional order differentiation of the time series, and then are used as the input of the clustering algorithm to cluster the time series. The simulation experimental results show that the new fractional-order similarity measure performs better compared with the clustering results based on the original distances.