Propagation Graph Estimation by Pairwise Alignment of Time Series Observation Sequences

Various things propagate through the medium of individuals. Some biological cells fire right after the firing of their neighbor cells, and such firing propagates from cells to cells. In this paper, we study the problem of estimating the firing propagation order of cells from the $\{0,1 \}$-state sequences of all the cells, where '1' at the $i$-th position means the firing state of the cell at time step $i$. We propose a method to estimate the propagation direction between cells by the sum of one cell's time delay of the matched positions from the other cell 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 correct for our synthetic datasets, and also to be consistent with visually recognizable firing order for the dataset of soil-dwelling amoeba's chemical signal emitting state sequences.