Manifold-based Bayesian inference for semi-supervised source localization

Sound source localization is addressed by a novel Bayesian approach using a data-driven geometric model. The goal is to recover the target function that attaches each acoustic sample, formed by the measured signals, with its corresponding position. The estimation is derived by maximizing the posterior probability of the target function, computed on the basis of acoustic samples from known locations (labelled data) as well as acoustic samples from unknown locations (unlabelled data). To form the posterior probability we use a manifold-based prior, which relies on the geometric structure of the manifold from which the acoustic samples are drawn. The proposed method is shown to be analogous to a recently presented semi-supervised localization approach based on manifold regularization. Simulation results demonstrate the robustness of the method in noisy and reverberant environments.