A PCA-based similarity measure for multivariate time series

Kiyoung Yang, C. Shahabi
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引用次数: 273

Abstract

Multivariate time series (MTS) datasets are common in various multimedia, medical and financial applications. We propose a similarity measure for MTS datasets, Eros Extended Frobenius norm), which is based on Principal Component Analysis (PCA). Eros applies PCA to MTS datasets represented as matrices to generate principal components and associated eigenvalues. These principal components and eigenvalues are then used to compare the similarity between MTS matrices. Though Eros in itself does not satisfy the triangle inequality, without which existing multidimensional indexing structures may not be utilized, the lower and upper bounds to satisfy the triangle inequality are obtained. In order to show the validity of Eros for similarity search on MTS datasets, we performed several experiments on three datasets (2 real-world and 1 synthetic). The results show the superiority of our approaches as compared to the traditional similarity measures for MTS datasets, such as Euclidean Distance (ED), Dynamic Time Warping (DTW), Weighted Sum SVD (WSSVD) and PCA similarity factor (SPCA) in precision/recall.
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基于pca的多变量时间序列相似性度量
多元时间序列(MTS)数据集在各种多媒体、医疗和金融应用中很常见。本文提出了一种基于主成分分析(PCA)的MTS数据集相似性度量方法——Eros Extended Frobenius norm。Eros将PCA应用于以矩阵表示的MTS数据集,生成主成分和相关特征值。然后使用这些主成分和特征值来比较MTS矩阵之间的相似性。虽然Eros本身不满足三角不等式,没有它就不能利用现有的多维索引结构,但得到了满足三角不等式的下界和上界。为了证明Eros在MTS数据集上相似性搜索的有效性,我们在三个数据集(2个真实数据集和1个合成数据集)上进行了几个实验。结果表明,与传统的MTS数据集相似度度量方法(如欧氏距离(ED)、动态时间扭曲(DTW)、加权和SVD (WSSVD)和PCA相似因子(SPCA))相比,我们的方法在精度/召回率方面具有优势。
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