  Modern neural recording techniques allow neuroscientists to obtain spiking
activity of multiple neurons from different brain regions over long time
periods, which requires new statistical methods to be developed for
understanding structure of the large-scale data. In this paper, we develop a
bi-clustering method to cluster the neural spiking activity spatially and
temporally, according to their low-dimensional latent structures. The spatial
(neuron) clusters are defined by the latent trajectories within each neural
population, while the temporal (state) clusters are defined by (populationally)
synchronous local linear dynamics shared with different periods. To flexibly
extract the bi-clustering structure, we build the model non-parametrically, and
develop an efficient Markov chain Monte Carlo (MCMC) algorithm to sample the
posterior distributions of model parameters. Validating our proposed MCMC
algorithm through simulations, we find the method can recover unknown
parameters and true bi-clustering structures successfully. We then apply the
proposed bi-clustering method to multi-regional neural recordings under
different experiment settings, where we find that simultaneously considering
latent trajectories and spatial-temporal clustering structures can provide us
with a more accurate and interpretable result. Overall, the proposed method
provides scientific insights for large-scale (counting) time series with
elongated recording periods, and it can potentially have application beyond
neuroscience.
