Bayesian Matrix Completion Under Geometric Constraints
This work addresses a fundamental challenge in signal processing for applications like sensor network localization and manifold learning, but it is incremental as it builds on existing geometric constraint methods.
The paper tackled the problem of completing Euclidean distance matrices from sparse and noisy observations by introducing a hierarchical Bayesian framework with structured priors, resulting in improved reconstruction accuracy in sparse regimes compared to deterministic baselines.
The completion of a Euclidean distance matrix (EDM) from sparse and noisy observations is a fundamental challenge in signal processing, with applications in sensor network localization, acoustic room reconstruction, molecular conformation, and manifold learning. Traditional approaches, such as rank-constrained optimization and semidefinite programming, enforce geometric constraints but often struggle under sparse or noisy conditions. This paper introduces a hierarchical Bayesian framework that places structured priors directly on the latent point set generating the EDM, naturally embedding geometric constraints. By incorporating a hierarchical prior on latent point set, the model enables automatic regularization and robust noise handling. Posterior inference is performed using a Metropolis-Hastings within Gibbs sampler to handle coupled latent point posterior. Experiments on synthetic data demonstrate improved reconstruction accuracy compared to deterministic baselines in sparse regimes.