基于高维空间的非线性降维的局部线性嵌入LLE方法

发布时间：2018-03-18 16:46

本文选题：线性降维　切入点：非线性降维　出处：《西南交通大学》2017年硕士论文　论文类型：学位论文

【摘要】：本文对于数据处理过程中常用的一些降维方法做了简单的分析介绍。首先,介绍了降维的主要概念以及数学定义,其中涉及到特征值问题以及优化问题,对于给定的一个高维空间数据集,对数据进行降维目的是将原来的高维空间进行压缩映射到低维空间当中,并且保持原始高维数据集的主要性质不变。当然,这其中还伴随着某些特征值问题。本文的主要任务之一是探索如何解决这些降维问题与优化问题,以及将高维数据如何可视化的研究;局部线性嵌入LLE方法是这篇文章主要研究的内容,并通过与线性降维方法的实例分析比较,从而分析了 LLE方法的优点及不足,且分析比较可以证明在实际应用中非线性降维还是很具实际意义的。本文的主要一个任务就是如何解决LLE方法其中存在的不足,并提出相应的改良方法。以下是提出了两种改进的LLE算法,对其参数的选择做出了一些改进,并且根据LLE方法不适用于稀疏非均匀数据集等的缺点,在方法优化中引入了加权矩阵的加权LLE方法,从而减小了方法的不适用性以及可适用性。此外,在样本点之间的距离应用测地距离而不是欧几里得距离来找到k个近邻的样本采集点,并通过公式验证了改进算法的可行性,以及此方法的有效性和实用性。
[Abstract]:In this paper, the data processing in some dimensionality reduction methods commonly used to do a simple introduction and analysis. Firstly, introduces the main concepts of dimensionality reduction and mathematical definition, which relates to the eigenvalue problem and the optimization problem for a given set of data in high dimensional space, dimension to the original high-dimensional space compression mapping into a low dimensional space of data, and keep the main properties of the original high dimensional data set unchanged. Of course, the value of these problems with certain characteristics. One of the main task of this paper is to explore how to solve the problem of dimensionality reduction and optimization problems, and study how to visualize high-dimensional data; local linear embedded LLE method is the main research content of this article, and by comparing practical dimensionality reduction method and linear analysis, and analyzes the advantages and shortcomings of LLE method, and compared with C In the practical application of nonlinear dimensionality reduction is very meaningful. One of the main task of this paper is how to solve the shortcomings of LLE method, and put forward the corresponding improvement method is put forward. The following two kind of improved LLE algorithm, the parameter selection has made some improvements, and sparse non uniform according to the data sets for the LLE method shortcomings, the weighted LLE method of weighted matrix is introduced in the optimization method, which reduces the applicability of the method and applicability. In addition, the distance between the sample points in the application of geodesic distance instead of Euclidean distance to find the sample point K and nearest neighbor. The feasibility of the algorithm is verified by the formula, and this method is effective and practical.

【学位授予单位】：西南交通大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：C812

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