Research And Implementation Of Manifold Learning Technology Based On Incremental

On the Mathematical Conference in 2000, Donoho made a speech about the trends of computer technology in the future. He thought data processing and analysis would be focused, and first proposed the concept “the curse of dimension” which meant the performance dropping dramatically as the dimensions increased. So, nonlinear dimension reduction technology became an important filed. Manifold learning, also called nonlinear dimension reduction, which handling data in a batch model, is not efficient to dynamic data system. This paper improves two classical manifold learning algorithms, such that can be applied to a wider range of case.This paper has deeply studied several classical manifold learning algorithms such as ISOMAP, LLE, LE and HLLE. We conclude a general framework for many manifold learning method. In addition, we have improved ISOMAP and LLE algorithms, and propose two increment algorithms of ISOMAP and LLE called InISOMAP and InLLE. The main works of this paper can be summarized as three aspects:First, this paper presents a general framework for many manifold learning algorithms. The main varieties of these methods are the structure of distance matrix of input data, normalized matrix and the optimal solutions to the eigen problem. In this way, the differences and similarities of each method can be easily analyzed.Second, this paper improved ISOMAP and LLE and proposed InISOMAP and InLLE. Each of these two methods preserves the global or local structure of input data. The experiments show that InISOMAP and InLLE output ISOMAP and LLE in dynamical data system.Third, this paper compares several current manifold learning algorthms with InISOMAP and InLLE. In the experiments, we a variety of data sampled from different manifolds to all the algorthms. Then the advantages and disadvantages of the algorithms are be analyzed.Finally, we summarized and analyzed all the work of this paper, and we make the future work prospect.