Dimension reduction on neural activity paves a way for unsupervised neural decoding by dissociating the measurement of internal neural state repetition from the measurement of external variable tuning. The Poisson Gaussian-process latent variable model (P-GPLVM) is a powerful tool to discover the low-dimensional latent structure for high-dimensional spike trains with minimum assumptions. This thesis extends the P-GPLVM to enable the latent variable inference of new data constrained by the previously learned smoothness and mapping information, thereby allowing the estimation of internal state repetition in new neural activity. A principled approach for analyzing temporally-compressed patterns of activity (i.e. population burst events (PBEs)), and metrics for assessing the new latent variables are described. From hippocampal neural activity during active maze exploration, P-GPLVM learns a latent space encoding animal position and context. By inferring the latent variables of new neural data during running, certain internal neural state is found repeated, validated by the similar running experiences encoded in its nearby neural trajectories of the training data manifold. Further, repetition of internal neural states can be measured for neural activity during PBEs, allowing the identification for versatile replay patterns. Thus, this extended P-GPLVM framework enables effective unsupervised decoding for neural activity both during behavior and during PBEs.