Local smoothing for manifold learning

We propose methods for outlier handling and noise reduction using weighted local linear smoothing for a set of noisy points sampled from a nonlinear manifold. Weighted PCA is used as a building block for our methods and we suggest an iterative weight selection scheme for robust local linear fitting together with an outlier detection method based on minimal spanning trees to further improve robustness. We also develop an efficient and effective bias-reduction method to deal with the "trim the peak and fill the valley" phenomenon in local linear smoothing. Synthetic examples along with several image data sets are presented to show that manifold learning methods combined with weighted local linear smoothing give more accurate results.