政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/54412
English  |  正體中文  |  简体中文  |  Post-Print筆數 : 27 |  Items with full text/Total items : 113303/144284 (79%)
Visitors : 50804011      Online Users : 765
RC Version 6.0 © Powered By DSPACE, MIT. Enhanced by NTU Library IR team.
Scope Tips:
  • please add "double quotation mark" for query phrases to get precise results
  • please goto advance search for comprehansive author search
    •  Adv. Search
    Home ‧ Login ‧ Upload ‧ Help ‧ About ‧ Administer Goto mobile version


    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/54412


    Title: 一種基於函數型資料主成分分析的曲線對齊方式
    A Curve Alignment Method Based on Functional PCA
    Authors: 林昱航
    Lin,Yu-Hang
    Contributors: 黃子銘
    林昱航
    Lin,Yu-Hang
    Keywords: 函數型資料分析
    對齊程序
    主成分分析
    functional data analysis
    registration procedures
    principal component analysis
    Date: 2011
    Issue Date: 2012-10-30 10:58:23 (UTC+8)
    Abstract: 函數型資料分析的是一組曲線資料，通常定義域為一段時間範圍。常見的如某一個地區人口在成長期的身高紀錄表或是氣候統計資料。函數型資料主要特色曲線間常有共同趨勢，而且個別曲線反應共同趨勢時也有時間和強度上的差異。本文研究主要是使用Kneip 和 Ramsay提出，結合對齊程序和主成分分析的想法作為模型架構，來分析函數型資料的特性。首先在對齊過程中，使用時間轉換函數(warping function)，解決觀測資料上時間的差異；並使用主成分分析方法，幫助研究者探討資料的主要特性。基於函數型資料被預期的共同趨勢性，我們可以利用此一特色作為各種類型資料分類上的依據。此外本研究會對幾種選取主成分個數的方法，進行綜合討論與比較。
    In this thesis, a procedure combining curve alignment and functional principal component analysis is studied. The procedure is proposed by Kneip and Ramsay .In functional principal component analysis, if the data curves are roughly linear combinations of k basis curves, then the data curves are expected to be explained well by principle component curves. The goal of this study is to examine whether this property still holds when curves need to be aligned. It is found that, if the aligned data curves can be approximated well by k basis curves, then applying Kneip and Ramsay`s procedure to the unaligned curves gives k principal components that can explain the aligned curves well. Several approaches for selecting the number of principal components are proposed and compared.
    Reference: [1]陳順宇著. 3th.台北市:華泰書局,2004[民93].
    [2]P.Craven and G.Wahba.Smoothing noisy data with spline functions:estimating the correct degree of smoothing by the method of generalized cross validation.Numerische Mathematik,31:377–403,1979.
    [3]A.Kneip and J.O.Ramsay.Combining registration and fitting for functional models.Journalofthe American Statistical Association,103,issue 483:1155–1165,2008.
    [4]Jostein Lillestol and Fridthj of Ollmar.Introduction and applications to financial electricity contracts.2003.
    [5]Ciprian M.Crainiceanu and A.Jerey Goldsmith.Bayesian functional data analysis using winbugs.Journal of Statistical Software,Volume 32,Issue11,January 2010.
    [6]J.O.Ramsay and Silverman.Applied Functional Data Analysis.NewYork:Springer,2002.
    [7]J.O.Ramsay and Silverman.Applied Functional Data Analysis 2th.NewYork:Springer,2005.
    [8]Georg Gr¨on Roberto Viviani and Manfred Spitzer.Functional principal component analysis of fMRI data human brain mapping.Human Brain Mapping,January 2005.
    [9]Larry L.Schumaker.Spline Functions:Basic Theory.John Wiley&Sons,Inc.,1981.
    [10]Subhash原著;呂金河編譯.臺中市:滄海,2005.
    Description: 碩士
    國立政治大學
    統計研究所
    99354028
    100
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0099354028
    Data Type: thesis
    Appears in Collections:[Department of Statistics] Theses

    Files in This Item:

    File SizeFormat
    index.html0KbHTML2375View/Open


    All items in 政大典藏 are protected by copyright, with all rights reserved.


    社群 sharing

    著作權政策宣告 Copyright Announcement
    1.本網站之數位內容為國立政治大學所收錄之機構典藏，無償提供學術研究與公眾教育等公益性使用，惟仍請適度，合理使用本網站之內容，以尊重著作權人之權益。商業上之利用，則請先取得著作權人之授權。
    The digital content of this website is part of National Chengchi University Institutional Repository. It provides free access to academic research and public education for non-commercial use. Please utilize it in a proper and reasonable manner and respect the rights of copyright owners. For commercial use, please obtain authorization from the copyright owner in advance.

    2.本網站之製作，已盡力防止侵害著作權人之權益，如仍發現本網站之數位內容有侵害著作權人權益情事者，請權利人通知本網站維護人員(nccur@nccu.edu.tw)，維護人員將立即採取移除該數位著作等補救措施。
    NCCU Institutional Repository is made to protect the interests of copyright owners. If you believe that any material on the website infringes copyright, please contact our staff(nccur@nccu.edu.tw). We will remove the work from the repository and investigate your claim.
    DSpace Software Copyright © 2002-2004  MIT &  Hewlett-Packard  /   Enhanced by   NTU Library IR team Copyright ©   - Feedback