Most time series clustering methods mainly focus on univariate time series (UTS). Compared with UTS, multivariate time series (MTS) consists of multiple components. Although interest in MTS clustering is increasing, its performance is far from satisfactory. Most traditional MTS clustering methods may have two limitations. First, they do not consider both the temporal features of each component and the relationship between the components. Second, they can only identify the local relationship between adjacent data, but cannot obtain long-distance global relationships and capture clusters of arbitrary shapes. In this paper, we develop a method for MTS clustering based on fuzzy cognitive maps (FCMs) and community detection, termed as MTSC-FCM-CD. To overcome the first limitation, we use FCM to represent MTS; FCM can extract temporal features while preserving the relationship between components in MTS. To overcome the second limitation, we use the community detection algorithm to cluster the global relations, which is different from the traditional nearest neighbor distance-based method. In the calculation process, the similarity between FCMs should be used to build a complex network. Existing methods calculate the similarity between FCMs, only considering the numerical characteristics but ignoring the topological structure. To solve this problem, we design a two-stage similarity measure to build a complex network. In comparison to the existing methods, the experimental results on twenty benchmark datasets demonstrate the effectiveness of MTSC-FCM-CD in MTS clustering.

中文翻译：

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基于模糊认知图和社区检测的多元时间序列聚类


大多数时间序列聚类方法主要关注单变量时间序列（UTS）。与 UTS 相比，多元时间序列 (MTS) 由多个组成部分组成。尽管人们对 MTS 聚类的兴趣日益浓厚，但其性能却远不能令人满意。大多数传统的 MTS 聚类方法可能有两个局限性。首先，他们没有考虑每个组件的时间特征以及组件之间的关系。其次，它们只能识别相邻数据之间的局部关系，而无法获得长距离的全局关系并捕获任意形状的簇。在本文中，我们开发了一种基于模糊认知图（FCM）和社区检测的 MTS 聚类方法，称为 MTSC-FCM-CD。为了克服第一个限制，我们使用FCM来表示MTS； FCM 可以提取时间特征，同时保留 MTS 中​​组件之间的关系。为了克服第二个限制，我们使用社区检测算法对全局关系进行聚类，这与传统的基于最近邻距离的方法不同。在计算过程中，应利用FCM之间的相似性来构建复杂的网络。现有方法计算FCM之间的相似度，仅考虑数值特征而忽略了拓扑结构。为了解决这个问题，我们设计了一个两阶段相似性度量来构建一个复杂的网络。与现有方法相比，在 20 个基准数据集上的实验结果证明了 MTSC-FCM-CD 在 MTS 聚类中的有效性。