Approach On Dimensionality Reduction Algorithms Based Optimization Of Local Neighborhood

With the development of the information technologies, resulting in high dimensionaldata, have been successfully applied to the "digital" in the world, such as analysis of spectralimage, geographic information system, computational biology genetics etc. High dimensionaldata,with high dimension and the complex information, have challenged the ability of thecomputer in soft and hardware. The traditional clustering, classification algorithms cannotmeet the need for high dimensional data. At this time, manifold learning has become theeffective way to solve the problem of the high dimensionality.Manifold learning aims to reduce the dimension of data by transforming the highdimension data into low dimensional manifold structure. It is an important method in machinelearning, and become the advanced technology of dimensionality reduction forhigh-dimensional data. It is widely used in many application fields, become a focus andhotspot in recent years. These methods are: Isometric Mapping Isomap, local tangent spacealignment (LTSA) and locally linear embedding (LLE) etc. Nonlinear dimensionalityreduction method is presented almost by all the local linear approximation. But in many cases,the sample point in high dimensional has complex data distribution, local subspace is difficultto meet the local approximate linearization assumptions, leading to the final effect ofdimension reduction is not ideal. In this case, the optimization of local neighborhood spacehas become the important aspect of manifold learning.This paper focuses on the locally linear embedding (LLE) algorithm and the localtangent space alignment (LTSA) algorithm; put forward the corresponding solution to theneighborhood optimization problems in manifold learning:(1) The classic study of locally linear embedding (LLE) algorithm, the algorithm ofextraction mechanism of global information and local information, a method is proposed forthe linear arrangement of neighborhood competition.(2) The classic study of local tangent space alignment (LTSA) algorithm, found the localneighborhood information shortage, short circuit and noise interference, dimension reductionseriously effect outcome, it is difficult to widely used in processing of real data. Analysis ofthe above problems, we can discovery that the classical dimensionality reduction algorithmsare using global fixed size of neighborhood. We propose a local optimization algorithm basedon compressed sensing, using high dimension space target neighbors sampling technology,build "release" model, adaptive get optimal subspace, also optimize the neighborhood element,make the data overall dimension reduction effect is more stable. Finally, the experiments have proved that the proposed methods are effective.