Recently there has been an increase in the studies on time-series data mining specifically time-series clustering due to the vast existence of time-series in various domains. The large volume of data in the form of time-series makes it necessary to employ techniques such as clustering to understand the data and to extract information and hidden patterns. The most important aspect of time-series clustering is the similarity measure used to compare a pair of time-series. In this paper, we develop a new similarity measure specifically for the task of time-series clustering. The proposed similarity measure is developed based on a combination of a simple representation of time-series, slope of each segment of time-series, and Euclidean distance with the capability to be implemented by the so-called dynamic time warping. We prove in this paper that the proposed distance measure is metric and thus indexing can be applied. For the task of clustering, the Particle Swarm Optimization algorithm is employed. We evaluate the proposed similarity measure by comparing it to three well-known existing similarity measures in terms of various criteria used for the evaluation of clustering performances. The results indicate that the proposed similarity measure outperforms the rest in almost every dataset used in this paper.

最近，由于各种领域中时间序列的广泛存在，对时间序列数据挖掘（特别是时间序列聚类）的研究有所增加。时间序列形式的大量数据使得有必要采用诸如聚类的技术来理解数据并提取信息和隐藏模式。时间序列聚类最重要的方面是用于比较一对时间序列的相似性度量。在本文中，我们专门针对时间序列聚类的任务开发了一种新的相似性度量。拟议的相似性度量是基于时间序列的简单表示，时间序列的每个片段的斜率以及欧几里得距离的组合而开发的，并且具有通过所谓的动态时间扭曲来实现的能力。我们在本文中证明了所提出的距离度量是公制的，因此可以应用索引。对于聚类任​​务，采用了粒子群优化算法。我们通过与用于评估聚类性能的各种标准进行比较，将拟议的相似性度量与三个已知的现有相似性度量进行比较，从而对其进行评估。结果表明，在本文使用的几乎每个数据集中，拟议的相似性度量均优于其余度量。