![]() In this study, we propose an alignment-based method of estimating state propagation relationship between a pair of individuals from their time series of observed states. By virtue of this simplicity, propagation relation estimation does not need such long time series. Contrary to the fact that these methods can deal with various kinds of influence, the state propagation treats only the influence of taking similar states with some delay. In these methods, a parameterized stationary model is assumed and long time series are needed for its parameter estimation. Granger causality 1 and transfer entropy 2 are well-known methods for investigating the causal relationship between time series, and their extensions and applications have been still energetically investigated 3– 5. The state propagation from one individual to another individual can be seen as a simple causal relationship between them. However, biological propagation such as cell firing has more ambiguous propagation rules, and propagation through the medium of human beings such as information and virus propagation is more complex. Physical propagation such as vibration and heat follows physical law. ![]() The objectives of such analyses are diverse from identification of the sources and the propagation routes to learning a propagation model for prediction. Sometimes, it is very important to analyze how things such as vibration, heat, cell firing, information, virus and etc, propagated.
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