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基于子序列全连接和最大团的时间序列模体发现算法

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  摘 要:针对时间序列模体发现算法计算复杂,并且无法发现多实例模体的问题,提出基于子序列全连接和最大团的时间序列模体发现(TSSJMC)算法。首先,使用快速时间序列子序列全连接算法求得所有子序列之间的距离,生成距离矩阵;然后,设置相似性阈值,将距离矩阵转化为邻接矩阵,构造子序列相似图;最后采用最大团搜索算法从相似图中搜索最大团,最大团的顶点对应的时间序列为包含最多实例的模体。在公开的时间序列数据集上进行实验,选用已有的能够发现多实例模体的Brute Force和Random Projection算法作为对比对象,分别从准确性、效率、可扩展性和鲁棒性对TSSJMC算法进行分析并获得了客观的评判结果。实验结果表明,与Random Projection算法相比,TSSJMC算法在效率、可扩展性和鲁棒性法方面均有明显优势;与Brute Force算法相比,TSSJMC算法发现的模体实例数量虽略低,但其效率和可扩展性都优于Brute Force算法。因此,TSSJMC是质量和效率相平衡的算法。
  关键词:时间序列;时间序列子序列;子序列连接;最大团;模体发现
  中图分类号: TP311.13
  文献标志码:A
  Abstract: Existing time series motif discovery algorithms have high computational complexity and cannot find multi-instance motifs. To overcome these defects, a Time Series motif discovery algorithm based on Subsequence full Joins and Maximum Clique (TSSJMC) was proposed. Firstly, the fast time series subsequence full join algorithm was used to obtain the distance between all subsequences and generate the distance matrix. Then, the similarity threshold was set, the distance matrix was transformed into the adjacency matrix, and the sub-sequence similarity graph was constructed. Finally, the maximum clique in the similarity graph was extracted by the maximum clique search algorithm, and the time series corresponding to the vertices of the maximum clique were the motifs containing most instances. In the experiments on public time series datasets, TSSJMC algorithm was compared with Brute Force algorithm and Random Projection algorithm which also could find multi-instance motifs in accuracy, efficiency, scalability and robustness. The experimental results demonstrate that compared with Random Projection algorithm, TSSJMC algorithm has obvious advantages in terms of efficiency, scalability and robustness; compared with Bruce Force algorithm, TSSJMC algorithm finds slightly less motif instances, but its efficiency and scalability are better. Therefore, TSSJMC is an algorithm that balances quality and efficiency.
  Key words: time series; time series subsequence; subsequence join; maximum clique; motif discovery
  0 引言
  時间序列是按时间顺序排列的、具有相等时间间隔的一系列数据的集合[1]。时间序列无处不在,使其在各个行业获得普遍的应用。例如金融领域的证券交易数据[2]、气象领域的气温气压数据[3]、工业领域的用电数据[4]、医学领域的脑电波和心电图数据[5-6]等。在时间序列数据挖掘的诸多问题中,时间序列模式发现是一个基础性问题。时间序列模式发现包括查找事先指定模式和预先未知的模式。查找事先指定模式的问题(即按内容查询)已有诸多解决方法[7-10]。然而,查找预先未知、重复出现的模式即时间序列模体发现(也称为时间序列的序列主题发现)问题则面临更多挑战[11]。模体发现对于时间序列挖掘具有重要意义,可以用于解决时间序列聚类、分类、关联规则发现等问题[12]。
  模体发现源于生物信息学,用于寻找脱氧核糖核酸(DeoxyriboNucleic Acid, DNA)序列中具有相似排列和功能的短核苷酸片段。2002年,Lin等[11]首次将“模体”一词引入时间序列,并提出时间序列模体发现的概念,此后出现了许多模体发现方法。第一类常见的时间序列模体发现算法采用近似离散化方法,该类算法先采用字符串聚集近似(Symbolic Aggregate Approximation, SAX)算法将时间序列进行离散并符号化,然后在压缩后的数据中寻找相似片段或者提取规则[13-14]。此类算法虽表现出良好的性能,但是SAX会对数据进行平均处理,可能丢失数据集中具有重要意义的峰、谷等信息。第二类常见的模体发现方法是采用聚类发现时间序列模体,先将时间序列进行分段,然后使用聚类算法进行模体发现[15-16]。Eamonn等[17]指出利用滑动窗口提取时间序列进行聚类挖掘是完全无意义的,因为通过滑动窗口平移提取的每个数据点对于整体贡献为一条直线。第三类时间序列模体发现算法基于概率方法,该类算法主要采用滑动窗口提取子序列,然后将投影算法作用于子序列得到候选模体,再将候选模体作为基准从原始序列中查找多条模体[18-19]。此类算法虽效率高,但涉及参数过多并且计算复杂。第四类算法是子序列连接的时间序列模体发现算法,该类算法通过子序列连接得到所有子序列的最近邻后,构建子序列相似图,再采用最大团或最近邻算法计算相似序列作为模体[20-21]。该类算法在子序列连接和最大团搜索中计算成本很高。   2017年Yeh等[1]使用快速傅里叶变换提高子序列全连接的速度,然后寻找每个子序列的1-最近邻(1-Nearest Neighbor, 1-NN),彼此间相似度最高的两子序列即为模体,该算法无法发现多实例模体。结合文献[1]中算法计算简单、速度快的优势,本文提出基于子序列全连接和最大团的时间序列模体发现(Time Series motif discovery based on Subsequence full Joins and Maximum Cliques, TSSJMC)算法以高效地发现等长的多实例模体。实验结果表明,本文算法能够快速、准确地发现多实例模体,同时对噪声具有较好的鲁棒性。
  4 结语
  针对时间序列模体发现算法计算复杂,并且无法发现多实例模体的问题,本文提出了一种计算简单并且能够发现多實例模体的基于子序列全连接和最大团的时间序列模体发现(TSSJMC)算法。该算法通过子序列全连接,构建子序列相似图,寻找图中的最大团三个步骤获得时间序列中的多实例模体。基于多个公开数据集的多组实验表明,本文提出的算法能够在较短时间内发现多条模体,并且具有高效性、准确性和更强的可扩展性和鲁棒性。文中算法发现的模体均为等长模体,未来我们将考虑发现不同长度的模体。
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