Tracking the Dimensions of Latent Spaces of Gaussian Process Latent Variable Models

Determining the number of latent variables, or the dimensions of latent states, is a ubiquitous problem in dimension reduction. In this paper, we introduce a novel sequential method that relies on the Bayesian approach to estimate the dimension of a latent space of a Gaussian process latent variable model. The proposed method also considers settings where the number of latent variables varies with time. To evaluate our methodology, we compared the estimated dimensions with the true dimensions as they vary with time. Results on synthetic data demonstrate that our method has a very good performance.