Latent process model for manifold learning

Abstract

In this paper, we propose a novel stochastic framework for unsupervised manifold learning. The latent variables are introduced, and the latent processes are assumed to characterize the pairwise relations of points over a high dimensional and a low dimensional space. The elements in the embedding space are obtained by minimizing the divergence between the latent processes over the two spaces. Different priors of the latent variables, such as Gaussian and multinominal, are examined. The Kullback-Leibler divergence and the Bhattachartyya distance are investigated. The latent process model incorporates some existing embedding methods and gives a clear view on the properties of each method. The embedding ability of this latent process model is illustrated on a collection of bitmaps of handwritten digits and on a set of synthetic data