基于DTW和LMNN的多维时间序列相似性分析方法

发布时间：2018-05-14 07:15

本文选题：多维时间序列 + 相似性度量　；参考：《浙江大学》2017年硕士论文

【摘要】：多维时间序列是现实中广泛存在的一种数据类型,因而对多维时间序列的分析和数据挖掘有着重要的意义。相似性度量作为多维时间序列分析的关键之一,现有的方法存在诸多不足。本文提出一种计算多维时间序列相似度的方法,将衡量单维时间序列相似度的DTW扩展至多维时间序列,并结合度量学习算法LMNN,进而得到对多维时间序列更好的相似性度量效果。本文主要的研究工作如下:(1)DTW是计算单维时间序列相似度的常用方法,其主要缺陷是存在奇异点和高时间复杂度的问题。本文首先针对DTW的奇异点问题提出一种改进方法:通过同时考虑时间序列的数值信息和梯度信息来构造新的特征,在不引入额外参数的条件下解决奇异点问题(称为SDTW)。然后,将特征提取和降维算法PLA与SDTW相结合来解决DTW的高时间复杂度问题(称为PLA-SDTW)。仿真对比实验验证了 SDTW在有效解决DTW奇异点问题的同时,能够提高度量的准确性。进一步地,在保证与SDTW近乎相同度量效果的同时,PLA-SDTW的时间消耗远远小于其他方法。(2)为了度量多维时间序列的相似性,需要将DTW从单维扩展到多维,并需要同时解决多个变量之间的相关性度量。度量学习方法(如常用的LMNN)能够从训练集学习得到特征空间中更好的距离度量准则。本文将DTW与LMNN相结合得到LMNN-DTW模型,用来度量多维时间序列的相似度。首先,使用基于马氏距离的DTW来度量多维时间序列的相似性,通过马氏矩阵来表示多个变量之间的相关性度量。然后,使用LMNN算法,通过最小化特定的损失函数,来优化得到马氏矩阵。仿真对比实验验证了 LMNN-DTW的效果与当前最好的LDML-DTW方法相近,且明显好于其他方法,从而证明了该模型的有效性和优越性。(3)考虑到前文提出的SDTW能够有效地解决DTW奇异点问题,且具有更好的度量准确性,因此用SDTW替换DTW,与LMNN结合得到LMNN-SDTW模型。仿真实验验证了 LMNN-SDTW的效果与当前最好的LDML-DTW方法相近,且优于LMNN-DTW,同时明显好于其他方法,从而证明了 LMNN-SDTW模型对多维时间序列相似性度量的优越性。
[Abstract]:Multi-dimensional time series is a widely existing data type in reality, so it is of great significance to the analysis and data mining of multidimensional time series. Similarity measurement is one of the key problems in multidimensional time series analysis. In this paper, a method to calculate the similarity of multidimensional time series is proposed. The DTW which measures the similarity of one-dimensional time series is extended to multi-dimensional time series, and the measurement learning algorithm LMNNs is combined to obtain a better similarity measurement effect for multi-dimensional time series. The main research work of this paper is as follows: 1 / 1 DTW is a common method to calculate the similarity of single dimensional time series. Its main defect is the existence of singularity and high time complexity. In this paper, an improved method is proposed to solve the singular point problem of DTW by taking into account the numerical and gradient information of time series at the same time to construct new features, and to solve the singular point problem without introducing additional parameters. Then, the feature extraction and dimension reduction algorithm PLA and SDTW are combined to solve the high time complexity problem of DTW (PLA-SDT WN). The simulation results show that SDTW can effectively solve the singular point problem of DTW and improve the accuracy of measurement. Furthermore, the time consumption of PLA-SDTW is much smaller than that of other methods while ensuring the same measurement effect as SDTW.) in order to measure the similarity of multidimensional time series, it is necessary to extend DTW from one-dimensional to multi-dimensional. We also need to solve the correlation measure of multiple variables at the same time. Metric learning methods, such as LMNNs, can obtain better distance metrics in feature spaces from training sets. In this paper, we combine DTW and LMNN to obtain the LMNN-DTW model, which is used to measure the similarity of multidimensional time series. Firstly, the DTW based on Markov distance is used to measure the similarity of multi-dimensional time series, and the correlation measure between multiple variables is represented by Markov matrix. Then, LMNN algorithm is used to optimize the Markov matrix by minimizing the specific loss function. The simulation results show that the effect of LMNN-DTW is close to that of the best LDML-DTW method, and it is obviously better than other methods, which proves the validity and superiority of the model. (3) taking into account the above mentioned SDTW, the singularity point problem of DTW can be solved effectively. And it has better measurement accuracy, so the LMNN-SDTW model is obtained by replacing DTW with SDTW and combining with LMNN. The simulation results show that the effectiveness of LMNN-SDTW is similar to that of the best LDML-DTW method, and is better than that of LMNN-DTW, and it is also better than other methods, which proves the superiority of LMNN-SDTW model in measuring the similarity of multidimensional time series.
【学位授予单位】：浙江大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O211.61

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