  We present Predictive Sparse Manifold Transform (PSMT), a minimalistic,
interpretable and biologically plausible framework for learning and predicting
natural dynamics. PSMT incorporates two layers where the first sparse coding
layer represents the input sequence as sparse coefficients over an overcomplete
dictionary and the second manifold learning layer learns a geometric embedding
space that captures topological similarity and dynamic temporal linearity in
sparse coefficients. We apply PSMT on a natural video dataset and evaluate the
reconstruction performance with respect to contextual variability, the number
of sparse coding basis functions and training samples. We then interpret the
dynamic topological organization in the embedding space. We next utilize PSMT
to predict future frames compared with two baseline methods with a static
embedding space. We demonstrate that PSMT with a dynamic embedding space can
achieve better prediction performance compared to static baselines. Our work
establishes that PSMT is an efficient unsupervised generative framework for
prediction of future visual stimuli.
