Improving the robustness of ISOMAP by de-noising

ISOMAP is a manifold learning based algorithm for dimensionality reduction, which is successfully applied to data visualization. However, there exists such limitation in classical ISOMAP that the algorithm is sensitive to noises, especially outliers. So in this paper an extended ISOMAP algorithm is put forward to solve the problem of sensitivity. The proposed algorithm follows the method of classical ISOMAP except that a preprocessing strategy is introduced to remove the noises and outliers. The likelihood of each point to be a noise or an outlier is quantified by carrying out weighted principal component analysis and box statistics method is adopted to distinguish clear points from noisy ones, then ISOMAP can be performed after de-noising. Experiments on noisy s-curve and noisy Swiss-roll data validate its efficiency for improving robustness.