Latent smooth skeleton embedding

Learning a smooth skeleton in a low-dimensional space from noisy data becomes important in computer vision and computational biology. Existing methods assume that the manifold constructed from the data is smooth, but they lack the ability to model skeleton structures from noisy data. To overcome this issue, we propose a novel probabilistic structured learning model to learn the density of latent embedding given high-dimensional data and its neighborhood graph. The embedded points that form a smooth skeleton structure are obtained by maximum a posteriori (MAP) estimation. Our analysis shows that the resulting similarity matrix is sparse and unique, and its associated kernel has eigenvalues that follow a power law distribution, which leads to the embeddings of a smooth skeleton. The model is extended to learn a sparse similarity matrix when the graph structure is unknown. Extensive experiments demonstrate the effectiveness of the proposed methods on various datasets by comparing them with existing methods.