【作者】 朱韬；

【导师】 张三同；

【作者基本信息】 北京交通大学 ， 交通信息工程及控制， 2009， 硕士

【摘要】 信息技术的发展使得人们所面对的数据变得越来越复杂。而数据本身往往是高维的数据,其内在规律的复杂性也超过了人们的感知能力,因而人眼很难进行辨识。而数据降维技术是解决这种问题的一种重要手段。该方法将原始数据对应的高维空间映射到低维,尽可能的保证数据间的几何关系和距离测度不变,这样不仅能在以后的相关计算中减少许多数据量,并能获得数据的主要特征。数据降维技术主要有线性和非线性两种。线性方法目前较为成熟,主要方法有主成分分析PCA和多维尺度分析MDS等,有较强的数学基础且实现较简单。但是线性方法无法表现数据的内在结构。流形学习方法是一种非线性方法,是目前的研究热点之一。主要的方法有等距映射Isomap、局部线性嵌入LLE、拉普拉斯映射LE、局部切空间排列LTSA等,对比传统的线性方法,流形学习方法能够有效地发现非线性高维数据的本质维数,利于进行维数约简和数据分析。本文研究流形学习算法在图像处理中的应用,对非线性降维的三种算法(等距映射Isomap、局部线性嵌入LLE、拉普拉斯映射LE)分别进行了仿真研究,分析和验证了每种方法的特性和相应结论。同时从算法思想差异、计算复杂度及降维效果等方面对三种方法做了相应的比较分析。在分析LLE的对于样本无法分辨的不足后,本文引入了一种有监督的局部线性嵌入方法(SLLE)。通过对原始的LLE和SLLE的仿真比较,得到SLLE方法有较好的分类能力。同时,针对LLE以及SLLE方法在样本点稀疏的情况下对于邻域点取值较敏感的缺点,本文提出了一种改进算法,改变样本间度量距离的计算方式,使得结果对邻域点取值不那么敏感。另外,将SLLE运用到人脸识别中,研究表明,采用SLLE相比于原始的LLE有较好的识别率。更多还原

【Abstract】 With the development of information technology, the data processing has been becoming more and more complex. The inner structure of the data is usually high-dimensional, so that people can hardly understand it by direct-viewing cognition. Dimension reduction is one of the important techniques to deal with high—dimensional data. It has the original data in a higher dimensional space mapped into a lower dimensional space that the geometrical relationship and the distance measurement among data can be kept unchanged. Thus, the data quantity in future relative calculation can be reduced, also the mainly feature of the data can be availed.The dimensional reduction can be divided into two classes - linear and nonlinear. Linear methods, represented by Principal Component Analysis (PCA), Multi -dimensional Scaling (MDS), etc, with their substantial mathematical foundation and simple implementation, has been developed maturely. However, it can not show the inner structure of the data in linear methods. Manifold learning, such as Isometric Mapping (Isomap), Locally Linear Embedding (LLE), Laplacian Eigenmaps (LE), Local Tangent Space Alignment (LTSA), is a kind of nonlinear method, the research on it is a focus these days. Compared with traditional linear method, manifold learning can discover the intrinsic dimensions of nonlinear high dimensional data effectively, helping researchers to reduce dimensionality and analyze data better.This thesis studies the image processing with the method of manifold learning algorithm, conducts simulation to prove the three kinds of non-linear dimensionality reduction technologies (Isomap, LLE, LE), and analysis the features and conclusions of each method; Also, this thesis gives a corresponding improvement analysis on three manifold learning algorithms from the aspects as differences of algorithm ideological, Computational complexity and the effect of dimensional reduction.Having analyzed the disadvantage of disable to the classification of samples by LLE, this paper has introduced a theory of Supervised Locally Linear Embedding (SLLE). Through the simulation work, SLLE algorithm proves its stronger ability to classify the different samples. Besides, the method of original LLE and SLLE are too sensitive for the number of nearest neighbors. This thesis uses a method to improve algorithm which changes the way to measure the distance between two samples. As the result shows, the improved algorithms are not so sensitive to the number of he nearest neighbors. Also, SLLE is applied in the face recognition in this thesis. The result shows that compare to the original LLE, using SLLE concludes a higher recognition rate.更多还原