Neighborhood smoothing embedding for noisy manifold learning

Manifold learning can discover the structure of high dimensional data and provides understanding of multidimensional patterns by preserving the local geometric characteristics. However, due to locality geometry preservation, manifold learning is sensitive to noise. To solve the noisy manifold learning problem, this paper proposes 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 sample data point and then computes the reconstruction matrix of the projections on the estimated surface. Experiments on synthetic data as well as real world patterns demonstrated 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.