Growing Locally Linear Embedding for Manifold Learning

Locally linear embedding is an effective nonlinear dimensionality reduction method for exploring the intrinsic characteristics of high dimensional data. This paper proposes a new manifold learning method, which is based on locally linear embedding and growing neural gas and is termed growing locally linear embedding (GLLE). GLLE overcomes the major limitations of the original locally linear embedding, which are intrinsic dimensionality estimation, selection of the number of nearest neighbors, and computational complexity. By embedding the topology learning mechanism in growing neural gas, the proposed GLLE algorithm preserves global topological structures and geometric characteristics of input patterns, which makes the projections more stable. The performed theoretical analysis and experimental simulations show that GLLE results in a faster learning procedure and a lower reconstruction error, which widens the applicability of manifold learning.