Self-organized Locally Linear Embedding for Nonlinear Dimensionality Reduction

Locally Linear Embedding (LLE) is an efficient nonlinear algorithm for mapping high-dimensional data to a low-dimensional observed space. However, the algorithm is sensitive to several parameters that should be set artificially, and the resulting maps may be invalid in case of noises. In this paper, the original LLE algorithm is improved by introducing the self-organizing features of a novel SOM model we proposed recently called DGSOM to overcome these shortages. In the improved algorithm, nearest neighbors are selected automatically according to the topology connections derived from DGSOM. The proposed algorithm can also estimate the intrinsic dimensionality of the manifold and eliminate noises simultaneously. All these advantages are illustrated with abundant experiments and simulations.