  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.
