高維數(shù)據(jù)降維與建模在過程中的應(yīng)用

化工論文編號(hào):HG213  論文字?jǐn)?shù):20751,頁數(shù):55

 目       錄

中文摘要  …………………………………………………………………………I
英文摘要  …………………………………………………………………………II
目錄  ………………………………………………………………………………Ⅲ
1、概述 ……………………………………………………………………………1
2、緒論 ……………………………………………………………………………4
 2.1 降維問題的提出    ……………………………………………………4
 2.1.1 降維分類     ………………………………………………………6
 2.1.2 降維的定義  ……………………………………………………….7
 2.1.3 維數(shù)禍根  ………………………………………………………….9
 2.1.4 高維空間的特殊性  ………………………………………………. 9
 2.1.5 本征維數(shù)  …………………………………………………………. 11
 2.2 降維方法的概述………………………………………………………. 12
 2.2.1 線性降維  …………………………………………………………. 12
 2.2.2非線性降維 ………………………………………………………….15
        2.3 BP神經(jīng)網(wǎng)絡(luò)基本原理…………………………………………………..19
       2.3.1 BP神經(jīng)元…………………………………………………………….20
       2.3.2 BP網(wǎng)絡(luò)……………………………………………………………….21
               2.3.3 最速下降法…………………………………………………………..25
3、化工過程中降維方法的應(yīng)用 …………………………………………………………..26
      3.1 主成分分析應(yīng)用………………………………………………………….. ….. 26
 3.1.1  工藝說明  …………………………………………………………..26
 3.1.2  符合說明  …………………………………………………………..27
 3.1.3  模型假設(shè)  …………………………………………………………..27
 3.1.4  變量設(shè)置  …………………………………………………………..28
 3.1.5  建立模型  …………………………………………………………..28
 3.1.6  模型分析  …………………………………………………………..29
 3.2  LLE的應(yīng)用   ………………………………………………………….33
  3.2.1 LLE領(lǐng)域點(diǎn)的個(gè)數(shù)和維數(shù)的確定…………………………………....34
  3.2.2 神經(jīng)網(wǎng)絡(luò)隱含層層數(shù)的確定………………………………………..43
 3.3 線性降維與非線性降維的比較…………………………………….. ....45
4、總結(jié)與展望 ……………………………………………………………………..48
致謝  ………………………………………………………………………………..49
參考文獻(xiàn)  …………………………………………………………………………..50
附錄…………………………………………………………………………………..53

摘要：高維數(shù)據(jù)，如生物數(shù)據(jù)、網(wǎng)絡(luò)數(shù)據(jù)及金融市場(chǎng)交易數(shù)據(jù)等，其處理面臨兩個(gè)問題：一是維數(shù)災(zāi)難問題，維數(shù)膨脹給高維數(shù)據(jù)中模型識(shí)別和規(guī)則發(fā)現(xiàn)帶來極大挑戰(zhàn)；二是維數(shù)的增長(zhǎng)又帶來“維數(shù)福音”，高維數(shù)據(jù)中蘊(yùn)藏的豐富信息中可產(chǎn)生解決問題的新的可能性。如何將高維數(shù)據(jù)表示在低維空間中，并由此發(fā)現(xiàn)其內(nèi)在結(jié)構(gòu)是高維信息簇處理研究的關(guān)鍵問題之一。降維方法作為克服“維數(shù)災(zāi)難”的有效手段，本文對(duì)降維過程的應(yīng)用進(jìn)行了深入的探討主要包括三部分：
 1．簡(jiǎn)要概述了高維空間處理領(lǐng)域的發(fā)展?fàn)顩r以及它所蘊(yùn)含的一些問題，如“維數(shù)災(zāi)難”問題、高維空間中的特殊性問題、高維數(shù)據(jù)本征維數(shù)問題等。同時(shí)對(duì)常用線性降維方法，主要是主成分分析原理和常用非線性降維方法，主要是局部線性嵌入方法（LLE）原理的介紹。
 2．給出了高維數(shù)據(jù)處理中降維方法在對(duì)苯二甲酸精餾過程中的一個(gè)應(yīng)用實(shí)例，給出了線性降維方法中主成分分析在此精餾過程中降維的處理過程及結(jié)論和非線性降維中LLE對(duì)該精餾過程進(jìn)行降維。
 3. 比較了三種預(yù)測(cè)因變量的方法的優(yōu)良，即BP神經(jīng)網(wǎng)絡(luò)，主成分分析與BP神經(jīng)網(wǎng)絡(luò)和LLE與BP神經(jīng)網(wǎng)絡(luò)，發(fā)現(xiàn)就含水量而言，LLE與BP最佳，主成分與BP次之，BP最差；而就醋酸含量而言BP最佳，主成分與BP次之，LLE與BP最差。
 關(guān)鍵詞：高維數(shù)據(jù)，降維，主成分分析，LLE，BP神經(jīng)網(wǎng)絡(luò)

Abstract: The high-dimensional data, such as biological data, network data and financial market trading data, its processing faces two problems: First, the curse of dimensionality problem, dimension expansion to the high-dimensional data, pattern recognition and rules of discovery bring great challenges; second dimension of growth brings " blessing of dimension ", high-dimensional data in the hidden wealth of information that can be created new possibilities to solve the problem which includes three parts:
 1.  A brief overview of high-dimensional space processing state of development, as well as it contains some of the issues, such as "dimension disaster" problem, the special high-dimensional space, high dimensional data intrinsic dimension and so on. At the same time commonly used linear dimension reduction methods, is mainly used principal component analysis theory and nonlinear dimensionality reduction methods, mainly locally linear embedding (LLE) principle of introduction.
 2. Gives the high-dimensional data processing method in dimensionality reduction distillation process of terephthalic acid in an application example, and gives a linear dimensionality reduction method, principal component analysis in this distillation process in the processing and dimensionality reduction conclusions, as well as Nonlinear dimensionality reduction of LLE to reduce the dimension of the distillation process.
 3. Comparison Good or bad of three methods to predict the dependent variable, that is the BP neural network, principal component analysis with BP neural network and LLE with BP neural network. If the Water content is dependent variable, LLE with BP is best, principal component analysis with BP is second and BP is worst, while the acetic acid content is dependent variable, BP is best, principal component analysis with BP is second andLLE with BP is worst.
Key words: high-dimensional data; dimensionality reduction; principal component analysis; LLE, BP neural network