摘 要：應(yīng)用主成分分析原理，以少數(shù)的綜合變量取代原有的多維變量，使數(shù)據(jù)結(jié)構(gòu)簡(jiǎn)化，把原指標(biāo)綜合成幾個(gè)主成分，再以這幾個(gè)主成分的貢獻(xiàn)率為權(quán)數(shù)進(jìn)行加權(quán)平均，構(gòu)造出一個(gè)綜合評(píng)價(jià)函數(shù)。本文以目前國(guó)家正在實(shí)施的免費(fèi)師范生政策為背景，對(duì)陜西師范大學(xué)的免費(fèi)師范生進(jìn)行了系統(tǒng)性的問(wèn)卷式抽樣調(diào)查，并對(duì)調(diào)查結(jié)果進(jìn)行整理統(tǒng)計(jì)和主成分分析，從而提取出免費(fèi)師范生生源變化的主要影響因素(即特征)。
本文所應(yīng)用的學(xué)科為模式識(shí)別，涉及到的理論方法是特征選擇與特征提取，同時(shí)深刻理解K-L變換的定義、概念，以及在特征提取中的應(yīng)用。
關(guān)鍵詞：主成分分析 綜合評(píng)估 特征選擇 特征提取

Based on Principal Component Analysis in the Various Source of Tuition-free Normal College Student
Gao Yuliang
(College of Computer Science，Shaanxi Normal University，
Xi′an 710062，Shaanxi， China)
Abstract: The theory of principle component analysis can use less comprehensive variables to instead of the multivariate variables, this method can simplify the structure of the data and aggregate the original index into several principal components.Regarding the contribution rate of this principal component as right, count weighted average and make up a comprehensive assessment function. The paper take the present country policy of Tuition-free Normal College Student as a background,then the students in the Shaanxi Normal University has been carried on a systematic questionnaire and it uses the theory to analysis the statistical results, thus extract the major effect factors(That is characteristic) to the changing source of tuition-free Normal College Student.
The related subjects is Pattern Recognition, in this process, the feature selection and extraction are also used. At the same time , according to the analysis, it needs to understand something as definitions, concepts of Karhunen-Loeve Transform and its application in feature extraction.
Key words: principle component analysis comprehensive assessment
feature selection feature extraction


1.緒論 4
1.1 課題的背景及提出的意義 4
1.1.1課題提出的背景 4
1.1.2課題提出的意義 4
1.2 研究現(xiàn)狀 4
1.2.1 主成分分析理論簡(jiǎn)介 4
1.2.2 理論原理及基本思想 5
1.2.3 主成分分析理論在實(shí)驗(yàn)研究的應(yīng)用情況 5
2.主成分分析的前提 6
2.1模式識(shí)別 6
2.2樣品與特征 6
2.3特征提取 6
2.4特征選擇 7
2.5 K-L變換 7
3.主成分分析的設(shè)計(jì)與實(shí)現(xiàn) 7
3.1基本概念 7
3.2主成分分析方法的設(shè)計(jì) 8
3.3主成分分析方法的計(jì)算步驟 10
3.4主成分分析方法的實(shí)例 10
3.5主成分分析方法的優(yōu)缺點(diǎn) 12
4.關(guān)于免費(fèi)師范生生源問(wèn)題分析 13
4.1研究方法 13
4.2生源分析過(guò)程 14
4.2.1原始數(shù)據(jù)的標(biāo)準(zhǔn)化處理 14
4.2.2計(jì)算相關(guān)系數(shù)矩陣 15
4.2.3計(jì)算R的特征值與特征向量 16
4.2.4確定主成分個(gè)數(shù) 16
4.2.5綜合評(píng)價(jià) 17
4.3計(jì)算機(jī)分析相關(guān)代碼 19
5 結(jié)論 21
結(jié)束語(yǔ) 21
附錄 【參考文獻(xiàn)】 21
致 謝 22