A Projective Noise Reduction Algorithm Based on Laplacian Smoothing

In order to avoid the curse of dimensionality, which is often encountered in big data analysis, manifold learning assumes that high-dimensional data is embedded in a low-dimensional smooth manifold. However, in practical applications, the data sets often contain inevitable noise, and the manifold learning algorithm itself is often sensitive to noise. Therefore, in order to reduce the interference of noise to the manifold learning algorithm, we propose a new projective noise reduction algorithm based on Laplacian smoothing. The main idea of this algorithm is to perform Laplacian smoothing on a data set before projection of the sample points, so that the data set can present expected manifold structure, which solves the problem that the sample points are too scattered and deviated from the main manifold well. In avoid of the over-smoothing problem caused by Laplacian smoothing algorithm, we propose to control the number of iterations based on the variance reduction. The experimental results show that the proposed algorithm can reduce the noise as well as maintain the manifold structure, and the noise reduction effect is superior to the traditional noise reduction algorithm.