基于二维奇异值分解的多元时间序列相似匹配方法

多元时间序列(Multivariate Time Series, MTS)广泛应用于医学、经济、多媒体等领域。针对其相似模式匹配问题，该文提出一种基于2维奇异值分解(Two-Dimensional Singular Value Decomposition, 2DSVD)的匹配方法。2DSVD是经典奇异值分解的扩展，能准确地描述MTS的本质特征。首先对MTS进行2DSVD分解；然后将MTS按行、列组成的协方差矩阵的主特征向量结合原MTS矩阵组成其模式表示矩阵，并借助Euclid范数来度量两个特征模式矩阵之间的相似程度，进而进行多元时间序列的模式匹配。最后通过与直接欧氏距离法、主成分分析、趋势距离、基于点分布特征4种相似匹配方法对3种不同数据规模的数据集进行对比实验，验证了所提方法刻画多种数据规模的多元时间序列特征的有效性和高效性。

Similar Pattern Matching Method for Multivariate Time Series Based on Two-dimensional Singular Value Decomposition

Multivariate Time Series (MTS) are used in very broad areas such as medicine, finance, multimedia and so on. A new method for similar pattern matching is proposed based on 2D Singular Value Decomposition (2DSVD). 2DSVD is an extension of standard SVD, which can explicitly describe the 2D nature of MTS. First, MTS is decomposed by 2DSVD. Second, the eigenvectors of row-row and column-column covariance matrix of MTS samples are computed for feature pattern matrix. Then, Eculid distance is adopted to measure the similarity between feature pattern matrix. Finally, through the comparison with directly Eculid distance, principal component analysis, trend distance and matching method based on point distribution for 3 different data sets, the experimental results show that it is easy to character the nature of MTS with this method, and with which various scales of series data can be processed more efficently.