Manifold Learning using Growing Locally Linear Embedding

Locally linear embedding (LLE) is an effective nonlinear dimensionality reduction method for exploring the intrinsic characteristics of high dimensional data. This paper mainly proposes a hierarchical framework manifold learning method, based on LLE and growing neural gas (GNG), named growing locally linear embedding (GLLE). First, we address the major limitations of the original LLE: intrinsic dimensionality estimation, neighborhood number selection and computational complexity. Then by embedding the topology learning mechanism in GNG, the proposed GLLE algorithm is able to preserve the global topological structures and hold the geometric characteristics of the input patterns, which make the projections more stable and robust. Theoretical analysis and experimental simulations show that GLLE with global topology preservation tackles the three limitations, gives faster learning procedure and lower reconstruction error, and stimulates the wide applications of manifold learning