高维数据降维方法及化工应用

论文编号:HG209  论文字数:12219,页数:30

摘要：本文选以小麦粉的红外光谱检测数据为研究对象，运用偏最小二乘降维技术，建立用于预测未知样品性质或组成的分析模型。NIR光谱区(700-2500nm) 主要是由含氢基团的倍频和组频吸收峰组成,吸收强度弱灵敏度相对较低 ,吸收带较宽且重叠严重,考虑到它属于弱光谱信号分析技术,所得信息受到许多因素影响，且作为信息源的近红外光谱中有效信息率低等，所以需要有效的方法来消除影响或降噪等，即降低光谱数据的维数，用以建立校正模型并预测未知样品性质或组成。目前使用的较多的建模方法有逐步回归法、主成分回归方法和偏最小二乘回归方法等等。本实验采用偏最小二乘(PLS)技术，建立NIR定量分析的多元校正模型，并用该模型预测样品数据。同时，实施主成分回归方法建模并预测，以验证两种不同方法的优劣。

关键词：降维；偏最小二乘；逐步回归；主成分分析；NIR

Abstract: In this paper,we choose the infrared spectral data of wheat flour as subject for the study,partial least squares dimension reduction technique is used to set analysis model for predicting the nature or the composition of unknown samples. NIR spectra of the district (700-2500nm) is mainly composed by the hydrogen-containing group and the frequency group of absorption peak,the absorption intensity is weak and sensitivity degree is relatively low, absorption range is wide and overlapping seriously,considering it belongs to the weak spectral signal analysis technology, information obtained is influenced by many factors, and as a source of information in the near-infrared spectroscopy there’s low rate of effective information, so we need effective ways to eliminate noise and other impacts or to reduce the dimension of spectral data for the establishment of calibration model and predict the nature or the composition of unknown samples. Currently used methods for modeling is stepwise regression, principal component regression and partial least-squares regression methods.This experiment use partial least squares (PLS)technology,and establish the multivariate calibration model for NIR quantitative analysis, and then use the model to predict the sample data. At the same time,implement  modeling and forecasting use principal component regression method,in order to verify the merits of two different methods.

Keywords：Dimension reduction;PLS;Stepwise regression;PCA
 目  录
中文摘要 I
英文摘要 II
目录 III
1. 绪论 1
 1.1 引言 1
 1.2 逐步多元线性回归技术研究进展 1
 1.3 主成分分析技术研究进展 1
 1.4 偏最小二乘技术研究进展 2
 1.5 NIR生物样品检测的现状 2
 1.6 本文的主要工作 3
2.多重共线性问题 4
 2.1 引言 4
 2.2 逐步多元线性回归 4
3. 主成分分析 5
 3.1 引言 5
 3.2 主成分分析的数学模型 5
 3.3 主成分分析的几何意义 6
 3.4 主成分分析的计算过程 7
 3.5 对主成分分析的讨论 9
 3.6 主成分回归建模 9
 3.7 实验小结 13
4. 偏最小二乘（PLS）回归 15
 4.1 引言 15
 4.2 偏最小二乘法 15
 4.2.1 基本概念 16
     4.2.2 基本模型 16
     4.2.3 非线性迭代偏最小二乘法 17
     4.2.4 SIMPLS算法 18
 4.2.5 本实验所用数学模型 19
 4.3 PLS用于小麦粉NIR分析 20
 4.4 实验小结 22
5.总结 23
致谢 24
参考文献 25