The brain encodes information by neural spiking activities, which can be described by time series data as spike counts. Latent Vari- able Models (LVMs) are widely used to study the unknown factors (i.e. the latent states) that are dependent in a network structure to modulate neural spiking activities. Yet, challenges in performing experiments to record on neuronal level commonly results in rela- tively short and noisy spike count data, which is insufficient to de- rive latent network structure by existing LVMs. Specifically, it is difficult to set the number of latent states. A small number of latent states may not be able to model the complexities of underlying sys- tems, while a large number of latent states can lead to overfitting. Therefore, based on a specific LVMs called Linear Dynamical Sys- tem (LDS), we propose a Reduced-Rank Linear Dynamical System (RRLDS) to estimate latent states and retrieve an optimal latent net- work structure from short, noisy spike count data. This framework estimates the model using Laplace approximation. To further handle count-valued data, we introduce the dispersion-adaptive distribution to accommodate over-/ equal-/ and under-dispersion nature of such data. Results on both simulated and experimental data demonstrate our model can robustly learn latent space from short-length, noisy, count-valued data and significantly improve the prediction perfor- mance over the state-of-the-art methods.