Dimensionality Reduction Based On Manifold Learning

Dimensionality reduction methods in the field of machine learning and data mining have a wide range of applications. The major algorithms are used as the method of data preprocessing. The algorithms greatly reduce the time and space complexity so the data reduction algorithms for machine learning become one of the hot research topics. Traditional dimensionality reduction methods can only process a the data set with linear structure but they are not applicable for the non-linear structure data set. Thus the study of nonlinear dimensionality reduc-tion methods aroused the interest of researchers. This paper studies nonlinear dimensionality reduction methods based on manifold learning. Manifold learning assume that the data points distributed in a smooth manifold. Then we want to preserve the intrinsic feature of the data set. And finally according to the spectral methods theory, the intrinsic feature can be best preserved and each point can obtain the corresponding low-dimensional representation.In this paper,we analysis the typical existing manifold learning methods and the theory of kernel function. we also kernelize the method of the Laplace eigen-maps. And then we try to integrate the linear method and nonlinear methods together in order to get a satisfactory result. And performing the algorithm on classical data sets and a challenging data set achieved good results. To further illustrate the effectiveness of the algorithm, this algorithm is applied to the classi-fication of handwritten characters and face classification algorithm as a preprocess and get satisfactory results. In order to ensure the effectiveness of this algorithm, the paper shows the further theoretical in-depth analysis.