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In recent years, data driven methods have been successfully used for analyzing multi-subject functional magnetic resonance imaging (fMRI) datasets. These methods attempt to learn shared spatial activation maps (SM) or voxel time courses (TC) from temporally or spatially concatenated fMRI datasets respectively. Most of the methods proposed so far do not distinguish whether a particular SM/TC is a group level component or only present in a certain subject dataset.

In recent history, dictionary learning (DL) methods have been successfully used for analyzing multi-subject functional magnetic resonance imaging. These algorithms try to learn group-level spatial activation maps (SM) or voxel time courses (TC) from temporally or spatially concatenated fMRI datasets respectively. However, in multi-subject fMRI studies, we are interested in both group-level TCs as well as SMs.

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.

Generative adversarial network (GAN) is a new idea for training models, in which a generator and a discriminator compete against each other to improve the generation quality. Recently, GAN has shown amazing results in image generation, and a large amount and a wide variety of new ideas, techniques, and applications have been developed based on it. Although there are only few successful cases, GAN has great potential to be applied to text and speech generations to overcome limitations in the conventional methods.