Bayesian Multiview Manifold Learning Applied to Hippocampus Shape and Clinical Score Data

Abstract

In this paper, we present a novel Bayesian model for manifold learning, suitable for data that are comprised of multiple modes of observations. Our data are assumed to be lying on a non-linear, low-dimensional manifold, modelled as a locally linear structure. The manifold local structure and the manifold coordinates are latent stochastic variables that are estimated from a training set. Through the use of appropriate prior distributions, neighbouring points are constrained to have similar manifold coordinates as well as similar manifold geometry. A single set of latent coordinates is learned, common for all views. We show how to solve the model with variational inference. We also exploit the multiview aspect of the proposed model, by showing how to estimate missing views of unseen data. We have tested the proposed model and methods on medical imaging data of the OASIS brain MRI dataset [6]. The data are comprised of four views: two views that correspond to clinical scores and two views that correspond to hippocampus shape extracted from the OASIS MR images. Our model is successfully used to map the multimodal data to probabilistic embedding coordinates, as well as estimate missing clinical scores and shape information of test data.