Nonlinear Dynamic Projection for Noise Reduction of Dispersed Manifolds

The search for a low-dimensional structure in high-dimensional data is one of the fundamental tasks in machine learning and pattern recognition. Manifold learning algorithms have recently emerged as alternatives to traditional linear dimension reduction techniques. In this paper, we propose a novel projection method that can be combined with any manifold learning methods to improve their dimension reduction performance when applied to high-dimensional data with a high level of noise. The method first builds a dispersion function that describes the distribution of dispersed manifold where the data lie. It then projects the noisy data onto a region wrapping the true manifold sufficiently close to it by applying a dynamical projection system associated with the constructed dispersion function. The effectiveness of the proposed projection method is validated by applying it to some real-world data sets with promising results.