Manifold constrained finite Gaussian mixtures

In many practical applications, the data is organized along a manifold of lower dimension than the dimension of the embedding space. This additional information can be used when learning the model parameters of Gaussian mixtures. Based on a mismatch measure between the Euclidian and the geodesic distance, manifold constrained responsibilities are introduced. Experiments in density estimation show that manifold Gaussian mixtures outperform ordinary Gaussian mixtures.