Locally Linear Minimum Spanning Trees for Manifold Learning

Graph-based manifold learning techniques have become of paramount importance when researchers have been faced to nonlinear data. These techniques have allowed them to discover relations that usual approaches such as PCA and MDS were incapable of. However, properties such as non-uniform sampling, varied topological substructures and highly curved manifolds still represent a challenge to these methods. We propose a graph building framework that strives at capturing the topological structures hidden in the data by means of a locality linear characterization combined with a MST-based noise model. We propose two algorithms under such framework that show improved performance over usual approaches.