  Sequences of correlated binary patterns can represent many time-series data
including text, movies, and biological signals. These patterns may be described
by weighted combinations of a few dominant structures that underpin specific
interactions among the binary elements. To extract the dominant correlation
structures and their contributions to generating data in a time-dependent
manner, we model the dynamics of binary patterns using the state-space model of
an Ising-type network that is composed of multiple undirected graphs. We
provide a sequential Bayes algorithm to estimate the dynamics of weights on the
graphs while gaining the graph structures online. This model can uncover
overlapping graphs underlying the data better than a traditional orthogonal
decomposition method, and outperforms an original time-dependent Ising model.
We assess the performance of the method by simulated data, and demonstrate that
spontaneous activity of cultured hippocampal neurons is represented by dynamics
of multiple graphs.
