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Study of Data Reduction Technique Based on Manifold Learning

Author: HuPeng
Tutor: YangAnPing
School: Changsha University of Science and Technology
Course: Traffic Information Engineering \u0026 Control
Keywords: manifold learning linear dimension reduction nonlinear dimensionality reduction graph embedding locally linear embedding geometric perturbation maximal linear patch
CLC: TP311.13
Type: Master's thesis
Year: 2011
Downloads: 16
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Abstract


The data in nature mostly in the form of high-dimensional and unstructured form existing. With the rapid development of information technology, it is possible to obtain these data . High dimensional data is not only difficult to people intuitively understand, but also to machine learning and data mining algorithms to deal with effectively. Dimensional-Reduction has become an important means of dealing with these data. After several years of development, dimensionality reduction technology has made great progress, there has been such as PCA, LDA and a series of classical methods. But in the present field of linear and nonlinear dimensionality reduction field, there are still many challenging issues. In the first decade of the 21st century, take ISOMAP、LLE as representation, manifold methods development advance rapidly. Become one of the most popular contemporary dimension reduction methods.Papers from the generalized definition of manifold learning starting, around the linear manifold and nonlinear dimensionality reduction algorithm expanded. From the global linear manifold reduction, nonlinear manifold global dimension reduction, Local nonlinear manifold dimensionality reduction, Carried out some research on the manifold learning algorithm.The main work of this dissertation can be summarized as follows:In order to solve the LDA“Small Sample”Large consumption calculation and memory requirements disadvantages. Take the traditional linear discriminant analysis method into the framework of graph embedded. Combined with regularization, a new LDA algorithm based on graph embedding and regularization. The unsupervised optimal class separate criterion have been built, then proposed a method to get this discriminant vector by graph embedding theory. At last, the complex Eigenvalue decomposition in the original LDA be convert to a simple eigenvalues decomposition and regularization fitting process.LLE algorithm is sensitive for the number of nearest neighbors, and fails on sparse source data. In order solve the problem, a LLE algorithm based on geometric perturbation have been proposed. At first, the original dataset have been set into some maximal linear patch according to the geometric distance perturbation. The LLE will be apply to this maximal linear patch to complete the embedding dimensional-reduction.

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