Data Dimension Reduction Study Based On Manifold Learning

With the rapid development of computer science and technology, It’s has Generated a large number of data. High-dimensional data is not only difficult to be intuitive to understand, and it is difficult to be dealed effectively with the existing machine learning and data mining algorithms. How to effectively use these massive high-dimensional data has become the means to compete in the Future commercial. Data dimensionality reduction algorithm is an important means to dealeffectively with these high-dimensional data. Data dimensionality reduction is an important tool for feature extraction, data dimension reduction plays more and more important role in Pattern Recognition.Manifold learning algorithm is developed in recent years and it is a nonlinear dimensionality reduction algorithm.In2000, J.B.TenenbaumSam, Roweis and Sam published two important articles on the manifold learning model on the same issue of Science magazine. Their respective manifold learning algorithms:Isomeitric Feature Mapping, and Locally Linear Embedding. It is the first time use of the manifold learning terminology,marking the main features of a nonlinear manifold learning methods of birth. After nearly12years development, many new manifold learning algorithm were Put forward, such as the LSTA, LE, Hessian LLE.Nuclear methods was used in manifold learning algorithms,such as Local Lnear Embedding, Laplace feature map also achieved great results. Promoting the manifold learning to become a hot issue in the field of machine learning. This paper focuses on manifold learning algorithm and its application about the linear algorithm, study the nonlinear algorithm (manifold learning algorithms) and other aspects of convection-shaped learning algorithm.Dimensionality reduction was used in many areas, and the gradual improvement of its mathematical foundations-differential geometry, manifold learning will play an important role in many areas. In the first chapter of this thesis we introduce the purpose of data dimension reduction and the background of manifold learning nonlinear of data dimensionality, and itt’s purpose and progress, and also introduces some basic concepts of the manifold learning methods. In the second chapter of this thesis, two classical linear dimensionality reduction algorithm were introduced,Principal Component Analysis and Linear Discriminant Analysis. In the third chapter introducesd the six kinds of classical manifold learning methods, including Multidimensional Scaling, Isometric Feature Mapping, Locally Linear Embedding,The LLE,Laplacian eignmap, the Hessian Of the LLE.Local Tangent Space Alignment. We would also analysis that these manifold learning the advantages and disadvantages of each method as well as their similarities and differences. The experimental results of six kinds of classical manifold learning algorithm in matlab are given as well as some analysis in the paper.In the Chapter IV of the paper, we put forward an Nystrom algorithm based on density clustering ideas to improve the accuracy of manifold learning methods.Nystrom algorithm is a classical mathematical approximation in the integral equation of the algorithm,it can be used in the data dimensionality of the approximation of the matrix, reducing a complex matrix operations in a large sample of the data dimensionality algorithm. It has been applied to some of the manifold learning algorithms, such as the MDS. Nystrom method is a randomly matrix sampling, it is Extract the set of sample, while reducing the amount of computation, but the problem is affected the accuracy. In this thesis, in the paper proposes an improved algorithm, this algorithm is applied to the manifold learning dimensionality reduction algorithm, used to improve the efficiency of manifold learning algorithms.Experiments were carried out in the large-scale data sets,it has made some exploratory results.