独立成分分析技术研究

论文编号:ZD1501  论文字数:20402，附外文翻译，答辩PPT

一、题目
 独立成分分析技术研究
二、指导思想和目的要求
 利用已有的专业知识，培养学生解决实际工程问题的能力；
 锻炼学生的科研工作能力和培养学生的团结合作攻关能力；
三、主要技术指标
   1. 研究独立成分分析算法；
   2. 完成演示程序
四、进度和要求
 第01周----第02周：英文翻译；
 第03周----第04周：学习主成分分析与独立成分分析技术；
 第05周----第10周：研究独立成分分析算法；
 第11周----第16周：设计演示程序；
 第17周----第18周：撰写毕业设计论文，论文答辩；
五、主要参考书及参考资料
[1]《Independent Component Analysis》 Aapo Hyvarinen, Juha Karhunen, Erkki Oja , Wiley-Interscience; 1 edition, 2001
[2]《Independent Component Analysis: A Tutorial Introduction 》 James V. Stone, A Bradford Book , 2004
[3]《Bayesian Reasoning and Machine Learning Hardcover》 David Barber Cambridge University Press  2012
学生  赵利君     指导教师  邢超     系主任 ___________

独立成分分析技术研究

摘 要

     主成分分析（Principal Components Analysis，PCA）是一种分析、简化数据集的技术。主成分分析的原理是设法将原来变量重新组合成一组新的相互无关的几个综合变量，同时根据实际需要从中可以取出几个较少的总和变量尽可能多地反映原来变量的信息的统计方法叫做主成分分析或称主分量分析，也是数学上处理降维的一种方法。
 独立成分分析(Independent Component Analysis ,简称ICA)或独立分量分析是一种利用统计原理进行计算的方法。它是一个线性变换,这个变换把数据或信号分离成统计独立的非高斯的信号源的线性组合。目前比较流行的ICA算法又Infomax算法（信息最大化）、FastICA算法（定点算法，Fixed-point、快速ICA算法），方法分类的依据主要是求取分离矩阵W的方法不同。
 计算最大似然估计时，假设了与之间是独立的，然而对于语音信号或者其他具有时间连续依赖特性（比如温度）上，这个假设不能成立。但是在数据足够多时，假设独立对效果影响不大，同时如果事先打乱样例，并运行随机梯度上升算法，那么能够加快收敛速度。
 在诸多ICA算法中，固定点算法 (也称FastlCA)以其收敛速度快、分离效果好被广泛应用于信号处理领域。该算法能很好地从观测信号中估计出相互统计独立的、被未知因素混合的原始信号。
 本论文对，独立成分分析的一个改进的梯度学习算法进行了分析，简称正交信息极大化算法(OrthogonalIn fomax,O rth-Infomax)这个算法综合了Infomax算法和Fixed-Point（不定点）算法的优点。从语音信号和fMRI信号两方面来比较这三个算法。就语音信号的分离准确度来说，Orth-Infomax算法具有最好的分离精度。对于真实的fMRI数据来说，Orth-Infomax算法具有最佳的估计脑内激活的时间动力学准确性。相应的做出了语音数据的实验结果和fMRI数据的实验结果。
 
 
 ICA的主要的应用是特征提取、盲源信号分离、生理学数据分析、语音信号处理、图像处理及人脸识别等。
 
 关键词：主成分分析，独立成分分析，最大似然估计，FastICA算法，ICA的应用
 独立成分分析技术研究
 
ABSTRACT

 Principal component Analysis, Principal Components Analysis, PCA) is a kind of Analysis, simplify the technology of data sets.Principal component analysis is often used to reduce the dimensions of the data sets, while keeping the characteristic of the largest contribution to the variance of a data set.This is by retaining low order principal component, ignore higher-order principal component.Principal component analysis (pca) is a statistical method of dimension reduction, it is by using a orthogonal transformation, the original random vector that are relevant to the component into its component is not related to the new random vector, this appears to be the original random vector on the algebra of covariance matrix transformation into a diagonal matrix, on the geometry of the original coordinate transformation into a new orthogonal coordinate system, make it points to sample points to spread the most open p orthogonal direction, and then to multidimensional variable system dimension, make it to a high precision system is transformed into low dimensional variables, then through constructing the proper value function, further the low-dimensional systems into one dimension.    The principle of principal component analysis is to try to into a new set of the original variables were independent of each other a few variables, at the same time, according to the actual need to take out a few less the sum of the variables as much as possible to reflect the original statistical methods of information called principal component analysis (or called principal component analysis, also is a kind of mathematical processing dimension reduction method.Independent Component Analysis (Independent Component Analysis, ICA) and Independent Component Analysis is a method of using statistics principle to compute.It is a linear transformation, the transformation or the data signal is separated into independent non-gaussian statistics linear combination of the signal source.At present more popular ICA algorithm and Infomax algorithm (information maximization), FastICA algorithm (fixed-point algorithm, Fixed - point, fast ICA algorithm), classification method is mainly based on different methods to calculate the separation matrix W.    To calculate the maximum likelihood estimation, hypothesis and between is independent, yet for speech signal or other time continuous dependence characteristics (such as temperature), the hypothesis cannot be established.But in enough data, assuming independent influence on the effect is not big, if disrupted the sample in advance at the same time, rising and run the stochastic gradient algorithm, then can accelerate the convergence speed.
 This paper analyses the FastICA algorithm, independent component analysis of an improved learning algorithm of gradient, hereinafter referred to as orthogonal information maximization algorithm (OrthogonalIn fomax, O RTH - Infomax) this algorithm combines Infomax algorithm and the advantages of Fixed - Point algorithm.From two aspects of speech signal and the fMRI signal to compare the three algorithms..In terms of speech signal separation accuracy, Orth - Infomax separation algorithm has the best accuracy.For real fMRI data, Orth - Infomax algorithm has the best dynamic accuracy estimate brain activation time.Corresponding to the voice and data of the experimental results and the experimental results of fMRI data.    In many ICA algorithm, fixed point algorithm (also called FastlCA) for its quick convergence rate, good separation effect is widely used in signal processing field.The algorithm can estimate the statistically independent of each other from the observed signals, mixed by unknown factors, the original signal.The ICA is the main application of the feature extraction, physiological data signal blind source separation, analysis, speech signal processing, image processing, face recognition, etc. Keywords: principal component analysis, independent component analysis, the maximum likelihood estimation, FastICA algorithm, the application of ICA

独立成分分析技术研究
目录

第一章 绪论 1
1.1独立成分分析的概述 1
第二章 主成分分析法 3
2.1主成分分析定义与概述 3
2.2主成分分析的发展史 4
2.3主成分分析基本思想 6
2.4主成分分析法的基本原理 7
2.5主成分分析法的计算步骤 8
2.6主成分分析法的优缺点 9
2.6.1优点 9
2.6.2缺点 9
第三章 独立成分分析技术 11
3.1独立成分分析定义及背景 11
3.2  ICA和投影法 12
3.3 ICA的分类 12
3.4 独立成分分析基本原理与发展 13
3.4.1基本模型 13
3.4.2 立性测度为依据，确定目标函数  13
第四章  独立成分分析算法 15
4.1独立成分分析算法与空间数据分析 15
4.2密度函数和线性变换 16
4.3 最大似然估计法 16
4.4 FastICA算法 18
4.4.1FastICA简介 18
4.4.2 FastICA算法的优点 18
4.4.3 FastICA算法的说明 19
4.5实验结果 20
4.5.1 语音数据的实验结果 20
4.5.2fMRI数据的实验结果 21
第五章  ICA的应用 24
5.1 在脑磁图(MEG)中分离非自然号 24
5.2 在金融数据中找到隐藏的因素 24
5.3自然图像中减少噪声 24
5.4人脸识别 25
5.5图像分离 26
5.6语音信号处理 28
第六章  全文总结 30
参考文献 31
致谢 33
毕业设计小结 34
独立成分分析技术研究

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