Noisy manifold learning using neighborhood smoothing embedding

Manifold learning is an important dimensionality reduction tool that discovers the structure of high dimensional data and provides understanding of multidimensional patterns in data mining, pattern recognition, and machine learning. Several manifold learning algorithms are applied to extract the intrinsic features of different prototypes in high dimensional space by preserving the local geometric characteristics. However, due to the locality geometry preservation, these manifold learning methods, including locally linear embedding (LLE), are sensitive to noise. To solve the noisy manifold learning problem, this paper proposes a Neighbor Smoothing Embedding (NSE) for noisy points sampled from a nonlinear manifold. Based on LLE and local linear surface estimator, the NSE smoothes the neighbors of each manifold data and then computes the reconstruction matrix of the projections on the principal surface. Experiments on synthetic data as well as real world patterns demonstrate that the suggested algorithm can efficiently maintain an accurate low-dimensional representation of the noisy manifold data with less distortion, and give higher average classification rates compared to others.