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.
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