Research On Dimensionality Reduction Method Of Constrained Maximum Variance Mapping

With the rapid development of science and technology, high-dimensional data is moreand more. Noise information contained in the high-dimensional data, diversity andcomplexity of statistical characteristics showed in the dataset make the people facing greatchallenges when analysis and processing the high-dimensional data. So far, researchers haveproposed much dimensionality reduction algorithm in the field of machine learning.There are two types in dimensionality reduction methods, one is a linear dimensionalityreduction method. Linear dimensionality reduction method can effectively deal with the linearstructure of the dataset, and it is difficult to find the nonlinear structure information hidden inthe dataset. Another class is nonlinear dimensionality reduction methods, such as manifoldlearning, Kernel methods, artificial neural networks. Manifold learning as a nonlineardimensionality reduction method, is an important branch appeared in the beginning of thiscentury. Manifold learning had attracted much attention due to effectively find and maintainthe intrinsic geometric structure of the high-dimensional data sets. Despite the late appearanceof manifold learning has developed rapidly, and has been widely applied to face recognition,data visualization, etc.This article is to continue thorough research in manifold learning, and proposing twodimensionality reduction methods based on manifold learning, and applied in face recognition,and to prove the effectiveness of the new algorithm by comparing the experimental to theother algorithms.The main work of this article is as follows:1. Analyze the dimensionality reduction algorithms based on manifold learning.2. Introduce constrained maximum variance mapping (CMVM) a supervised weight,and proposed a supervised constrained maximum variance mapping algorithm(SCMVM).SCMVM use of local manifolds and label information of the sample to define a newrelationship weight, take the weight into algorithms effectively improve the rate of facerecognition.3. Proposed algorithm with the penalty parameter in supervision constrained maximumvariance mapping (PSCMVM). This algorithm draws on the idea of the penalty function inthe locality preserving mapping (LPP), to punish the variation of the samples indimensionality reduction, to preserve the local manifold.