Noise-Removal Method for Manifold Learning

Manifold learning algorithms are nonlinear dimensionality reduction methods which could find the intrinsic geometry structure of the data points and recover the latent main factors that influence object changes. However, noise is unavoidable for datasets in the process of sampling. The noisy data easily get wrong results when using manifold learning algorithms. This paper proposes a noisy-data pre-processing method for manifold learning algorithms. Firstly, we utilize shrink strategy and adopt the eigenvalue linear criterion to find the tangent hyperplane of each data point. Then, we construct the local coordinate system for each tangent hyperplane and get the projection coordinates of each data point. Finally, we reconstruct the high-dimensional coordinates of each data point by affine transformation. The experiments show that the proposed method is effective and useful.