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Local Linear Embedded LLE Method For Nonlinear Dimension Reduction Based On High Dimensional Space

Posted on:2018-06-22Degree:MasterType:Thesis
Country:ChinaCandidate:Y MaFull Text:PDF
GTID:2347330515471035Subject:Statistics
Abstract/Summary:PDF Full Text Request
In this paper,the data processing process commonly used in some of the methods to do a simple analysis of the introduction.Firstly,the main concepts and mathematical definitions of dimensionality reduction are introduced,which involves the eigenvalue problem and the optimization problem.For a given high-dimensional spatial data set,the purpose of reducing the data is to compress the original high-dimensional space To low-dimensional space,and to maintain the original high-dimensional data set of the main properties of the same.Of course,this is accompanied by some eigenvalue problem.One of the main tasks of this paper is to explore how to solve these problem of reduction and optimization,and how to visualize the high-dimensional data research;local linear embedded LLE method is the main content of this article,and with the linear dimensionality reduction method This paper analyzes the advantages and disadvantages of the LLE method,and it can be proved that the nonlinear dimensionality reduction is still very practical in practical application.The main task of this paper is how to solve the LLE method which has the shortcomings,and put forward the corresponding improvement method.In this paper,two improved LLE algorithms are proposed,and some improvements are made to the selection of their parameters.According to the shortcomings of LLE method which is not suitable for sparse nonuniform data sets,weighted LLE method of weighting matrix is introduced in method optimization,Thereby reducing the applicability of the method and applicability.In addition,the distance between the sample points is measured by the geodesic distance rather than the Euclidean distance to find the sample collection points of k neighbors,and the feasibility of the improved algorithm and the validity and practicability of the method are verified by the formula.
Keywords/Search Tags:Linear dimensionality reduction, Nonlinear dimensionality reduction, High dimensional data, Local linear embedding, Principal component analysis, Mapping
PDF Full Text Request
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