Robust Nonlinear Dimensionality Reduction for Manifold Learning

This paper proposes an effective preprocessing procedure for current manifold learning algorithms, such as LLE and ISOMAP, in order to make the reconstruction more robust to noise and outliers. Given a set of noisy data sampled from an underlying manifold, we first detect outliers by histogram analysis of the neighborhood distances of data points. The linear error-in-variables (EIV) model is then applied in each region to compute the locally smoothed values of data. Finally a number of locally smoothed values of each sample are combined together to obtain the global estimate of its noise-free coordinates. The fusion process is weighted by the fitness of EIV model in each region to account for the variation of curvatures of the manifold. Experimental results demonstrate that our preprocessing procedure enables the current manifold learning algorithms to achieve more robust and accurate reconstruction of nonlinear manifolds