Various things propagate through the medium of individuals. Some individuals follow the others and take the states similar to their states a small number of time steps later. In this paper, we study the problem of estimating the state propagation order of individuals from the real-valued state sequences of all the individuals. We propose a method to estimate the propagation direction between individuals by the sum of the time delay of one individual's state positions from the other individual's matched state position averaged over the minimum cost alignments and show how to calculate it efficiently. The propagation order estimated by our proposed method is demonstrated to be significantly more accurate than that by a baseline method for our synthetic datasets, and also to be consistent with visually recognizable propagation orders for the dataset of Japanese stock price time series and biological cell firing state sequences.

翻译：各种事物通过个人媒介传播。 一些人跟随其他人, 采取与他们州相类似的州, 之后采取一些小步骤。 在本文中, 我们根据所有个人的实际价值序列来研究个人的国家传播顺序问题。 我们提出一种方法来估计个人之间的传播方向, 估计个人国家立场与另一个人相匹配的州地位之间的时间延迟总和, 平均以最低成本对齐为单位, 并显示如何有效地计算。 我们拟议方法估计的传播顺序比我们合成数据集的基准方法要准确得多, 也符合日本股票价格时间序列和生物细胞点火状态序列数据设定的目视可识别的传播命令 。