Rank priors for continuous non-linear dimensionality reduction

Discovering the underlying low-dimensional latent structure in high-dimensional perceptual observations (e.g., images, video) can, in many cases, greatly improve performance in recognition and tracking. However, non-linear dimensionality reduction methods are often susceptible to local minima and perform poorly when initialized far from the global optimum, even when the intrinsic dimensionality is known a priori. In this work we introduce a prior over the dimensionality of the latent space that penalizes high dimensional spaces, and simultaneously optimize both the latent space and its intrinsic dimensionality in a continuous fashion. Ad-hoc initialization schemes are unnecessary with our approach; we initialize the latent space to the observation space and automatically infer the latent dimensionality. We report results applying our prior to various probabilistic non-linear dimensionality reduction tasks, and show that our method can outperform graph-based dimensionality reduction techniques as well as previously suggested initialization strategies. We demonstrate the effectiveness of our approach when tracking and classifying human motion.