【作者】 刘佳；

【导师】 吴清；

【作者基本信息】 河北工业大学 ， 模式识别与智能系统， 2006， 硕士

【摘要】 目前人类社会日益深入到信息时代,在进行科学研究的过程中,不可避免地会遇到大量的高维数据。降维是处理高维数据的一种有效手段,它的目的是找出隐藏在高维数据中的低维结构。降维算法大致可分为线性和非线性两类,PCA和Isomap分别为这两类算法的代表算法。主成分分析法(PCA)是一种常用的线性降维算法,它实现简单,可以确保发现处于高维向量空间的线性子空间上的数据集的真实几何结构,但是该算法的线性本质使其无法揭示复杂的非线性流形;Isomap算法是具有代表性的一种非线性降维算法,它是一种全局优化算法,该算法建立在经典多维尺度算法CDMS基础之上,试图保持数据间内在的几何特性,即保持数据点之间的测地线距离。本文就这两种算法进行了研究分析,重点放在对Isomap算法的研究讨论及其应用。本文工作主要包括:1)在降维理论的基础上,对线性降维算法主成分分析法(PCA)、非线性降维算法Isomap及其改进算法S-Isomap进行了研究和分析。同时,分别对PCA算法和Isomap算法、Isomap算法和S-Isomap算法进行了应用实例分析。2)研究分类算法中的代表算法——支持向量机。分别从SVM的原理、数学模型及其构造几个方面对SVM进行了研究。3)将Isomap算法与支持向量机相结合,进行脑电产生源分类的仿真实验。在仿真过程中,主要检测Isomap算法的降维能力、容噪性能和对分类仿真结果的影响等,并对仿真结果进行分析。更多还原

【Abstract】 Scientists are working with large volumes of high-dimensional data in informational era. Dimensionality reduction is an important technique, finding meaningful low-dimensional structures hidden in their high-dimensional observations.The algorithms of dimensionality reduction can be classified into two categories: linear and nonlinear dimensionality reduction method. PCA, a linear dimensionality reduction method, is simple to implement, and guaranteed to discover the true structure of data lying on or near a linear subspace of the high-dimensional input space. But this algorithm cannot solve nonlinear problem.As a representational algorithm of nonlinear dimensionality reduction methods, Isomap is a global optimal algorithm. It builds on CDMS but seeks to preserve the intrinsic geometry of data, as captured in the geodesic manifold distances between all pairs of data points. In this paper we research the two method, and importantly study and discuss Isomap and its application .The main work of this paper include:1) On the basis of dimensionality reduction theory, we research and analyze the linear dimensionality reduction technique such as Principal Component Analysis (PCA), and nonlinear dimensionality reduction methods, such as Isometric Mapping (Isomap) and S-Isomap . Then, we respectively analyze the instance of PCA and Isomap,Isomap and S-Isomap.2) We importantly study Support Vector Machine method, including the principle, the mathematical model and structure of SVM.3) We do the emulation experiment of EEG generation source by combing Isomap and SVM. In our experimentation, the main work is to test the dimensionality reduction ability of Isomap, the tolerant capability to noise, and the infection to the result, and to analyze the result of the emulation experiment.更多还原