时间序列匹配的时间扭曲编辑距离与刚度调整
Time Warp Edit Distance with Stiffness Adjustment for Time Series Matching
摘要：
以类似于串到串校正问题的方式，我们根据时间序列到时间序列校正问题来解决时间序列相似性，其中两个时间序列之间的相似性被测量为将一个时间序列转换为另一个时间序列所需的“编辑操作”的最小成本序列。为了定义“编辑操作”，我们使用图形编辑过程的范例，并最终得到一个动态规划算法，我们称之为时间扭曲编辑距离（TWED）。TWED在形式上与动态时间弯曲、最长公共子序列或带实惩罚的编辑距离算法略有不同。特别是，它突出了一个参数，该参数驱动一种沿时间轴的弹性测度的刚度。我们表明，TWED提供的相似性是一个度量可能有用的时间序列检索应用程序，因为它可以受益于三角不等式属性，以加快检索过程，同时调整参数的弹性措施。在这种情况下，一个下界推导出的时间序列到下采样的表示空间的匹配到原始空间的匹配。经验质量的TWED距离上一个简单的分类任务进行评估。与编辑距离、动态时间弯曲、最长公共子序列和带实际惩罚的编辑距离相比，TWED在所考虑的实验任务上被证明是相当有效的。
英文摘要：
In a way similar to the string-to-string correction problem we address time series similarity in the light of a time-series-to-time-series-correction problem for which the similarity between two time series is measured as the minimum cost sequence of "edit operations" needed to transform one time series into another. To define the "edit operations" we use the paradigm of a graphical editing process and end up with a dynamic programming algorithm that we call Time Warp Edit Distance (TWED). TWED is slightly different in form from Dynamic Time Warping, Longest Common Subsequence or Edit Distance with Real Penalty algorithms. In particular, it highlights a parameter which drives a kind of stiffness of the elastic measure along the time axis. We show that the similarity provided by TWED is a metric potentially useful in time series retrieval applications since it could benefit from the triangular inequality property to speed up the retrieval process while tuning the parameters of the elastic measure. In that context, a lower bound is derived to relate the matching of time series into down sampled representation spaces to the matching into the original space. Empiric quality of the TWED distance is evaluated on a simple classification task. Compared to Edit Distance, Dynamic Time Warping, Longest Common Subsequnce and Edit Distance with Real Penalty, TWED has proven to be quite effective on the considered experimental task.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
