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題名 貝氏曲線同步化與分類
Bayesian Curve Registration and Classification
作者 李柏宏
Lee, Po- Hung
貢獻者 黃子銘
Huang, Tzee-Ming
李柏宏
Lee,Po- Hung
關鍵詞 函數型資料分析
曲線同步化
曲線區別分析
馬可夫鏈蒙地卡羅法
function data analysis
curve registration
curve discrimination
Markov chain Monte Carlo method
日期 2009
上傳時間 9-May-2016 11:40:08 (UTC+8)
摘要 函數型資料分析為近年發展的統計方法。函數型資料是在一段特定時間上，我們只在離散的時間點上收集觀測值。例如:氣象觀測站所收集到的每月氣溫、雨量資料，即是一種常見的函數型資料。函數型資料主要有三種特色，共同趨勢性、觀測個體反應強度不同，觀測個體時間特色上的差異。本文研究主要是使用，Brumback與Lindstrom在2004所提出的自模型迴歸族(self-modeling)當作模型架構來處理函數型資料的趨勢性與個體反應強度。而為了處理函數型資料的時間差異性，我們在模型中加入時間轉換函數(time transformation function)，處理函數型資料的時間差異性步驟，這個過程稱為同步化。經過同步化的處理後，能幫助研究者更清楚資料的特性。模型中除了時間轉換函數的部份，其餘模型中的參數我們是利用馬可夫鏈蒙地卡羅法中的Gibbs Sampling來進行參數的抽樣，並以取出的抽樣值來估計參數。時間轉換函數的部份，我們使用概似懲罰函數(penalized likelihood function)來估計時間轉換函數的參數部份。由於函數型資料擁有趨勢性，我們預期不同類別的資料，會呈現不同的趨勢性，我們將利用此一特色當做分類上的標準。
      關鍵詞:函數型資料分析、曲線同步化、曲線區別分析、馬可夫鏈蒙地卡羅法。
Functional data are random curves observed in a period of time at discrete time points.They often exhibit a common shape, but with variations in amplitude and phase across curves.To estimate the common shape,some adjustment for synchronization is often made,which is also known as time warping or curve registration.In this thesis,splines are used to model the warping functions and the common shape. Certain parameters are allowed to be random.For the estimation of the random parameters,priors are proposed so that samples from the posteriors can be obtained using Markov chain Monte Carlo methods.For the estimation of non-random parameters, a penalized likelihood approach is used. It is found via simulation studies that for a set of random curves with a common shape,the estimated common shape function looks like the true function up to a location-scale transform,and the curve alignment based on estimated time warping functions looks reasonable.For two groups of random curves which differ in the group common shape functions,synchronization also improves the discrimination between groups in some cases.
     
     Key words: functional data analysis,curve registration,curve discrimination,markov chain monte carlo method.
參考文獻 [1] Anderson, C. W.,Stolz, E. A.,and Shamsunder, S., Multivariate autoregressive
     models for classication of spontaneous electroencephalogram during mental tasks.
     IEEE Transactions on Biomedical Engineering, 45:277{286, 1998.
     [2] Brumback, L. C.,Lindstrom, M. J., Self modeling with
     exible, random time transformations.
     Biometrics, 60(2):461{470, 2004.
     [3] Buner, F.,Biau, G.,and Wegkamp, M. H., Functional classication in hilbert spaces.
     IEEE Transactions on Information Theory, 51:2163{2172, 2005.
     [4] Deboor, C., A Practical Guide to Splines. Springer-Verlag Berlin and Heidelberg
     GmbH & Co. K, 1978.
     [5] Carroll, R. J.,Ruppert, D., Spatially-adaptive penalties for spline tting. Australian
     and New Zealand Journal of Statistics, 42:205{223, 2000.
     [6] Conan-Guez, B.,Rossi, F., Phoneme discrimination with functional multilayer perceptron.
     In D. Banks, L. House, F. R. McMorris, P. Arabie, and W. Gaul, editors,
     Classication, Clustering, and Data Mining Applications (Proceedings of IFCS
     2004), pages 157{165, Chicago, Illinois, July 2004. IFCS, Springer.
     [7] Fleet, S. L.,Glendinning, R. H., Classifying non-uniformly sampled vector-valued
     curves. Pattern Recognition, 37:1999{2008, 2004.
     [8] Gareth, M. J., Curve alignment by moment. Annals of Applied Statistics, 1:480{501,
     2007.
     [9] Gasser, T.,Kneip, A., Searching for structure in curve samples. Journal of the
     American Statistical Association, 90:1179{1188, 1995.
     [10] Gelman, A.,Rubin, D. B., Inference from iterative simulation using multiple sequences.
     Statistical Science, 7:457{511, 1992.
     [11] Geweke, J., Evaluating the accuracy of sampling-based approaches to the calculation
     of posterior moments (Disc: P189-193). In J. M. Bernardo, J. O. Berger,
     A. P. Dawid, and Smith, editors, Bayesian Statistics 4. Proceedings of the Fourth
     Valencia International Meeting, pages 169{188. Clarendon Press [Oxford University
     Press], 1992.
     [12] Heidelberger, P.,Welch, P. D., Simulation run length control in the presence of an
     initial transient. Operations Research (INFORMS), 31:1109{1144, 1983.
     [13] James, G. M.,Hastie, T. J., Functional linear discriminant analysis for irregularly
     sampled curves. Journal of the Royal Statistical Society Series B, 63:533{550, 2001.
     [14] Jank, W.,Shmueli, G., Functional data analysis in electronic commerce research.
     Statistical Science, 21(2):155{166, 2006.
     [15] Kneip, A.,Gasser, T., Convergence and consistency results for self-modeling nonlinear
     regression. The Annals of Statistics, 16:82{112, 1988.
     [16] Lang, S.,Brezger, A., Bayesian p-splines. Journal of Computational and Graphical
     Statistics, 13:183{212, 2004.
     [17] Naya, S., Cao, R., Artiaga, R., and García, A., New Method for Material Classication
     from TGA Data by Nonparametric Regression . Materials Science Forum,514{
     516:1452{1456,2006.
     [18] Ogden, R. T.,Miller, C. E.,Takezawa, K.,Ninomiya, S., Functional regression in
     crop lodging assessment with digital images. Journal of Agricultural, Biological,
     and Environmental Statistics, 7(3):389{402, 2002.
     [19] Poskitt, D.,Presnell, B.,and Hall, P., A functional data-analytic approach to signal
     discrimination. Technometrics, 23:73{102, 2001.
     [20] Ramsay, J. O.,Li, X., Curve registration. Journal of the Royal Statistical Society,
     Series B: Statistical Methodology, 60:351{363, 1998.
     [21] Rossi, F.,Conan-guez, B., Functional multi-layer perceptron: a nonlinear tool for
     functional data analysis. In Neural Networks, pages 45{60, 2005.
     [22] Rossi, F.,Villa, N., Support vector machine for functional data classication. EEG
     NEUROCOMPUTING, 69:730-742, 2006.
     [23] Silverman, B. W., Incorporating parametric effects into functional principal components
     analysis. Journal of the Royal Statistical Society, Series B: Methodological,
     57:673{689, 1995.
     [24] Silverman, B. W.,Ramsay, J. O., Functional Data Analysis. Berlin:Springer-Verlag,
     1997.
     [25] Silverman, B. W.,Ramsay, J. O., Applied Functional Data Analysis:Methods and
     Case Studies. Berlin:Springer-Verlag, 2002.
     [26] Wang, X.,Rossi, N.,Ramsay, J. O., Nonparametric item response function estimates
     with the EM algorithm. J. Educational and Behavioral Statistics, 27:291{317, 2002.
描述 碩士
國立政治大學
統計學系
96354020
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0096354020
資料類型 thesis
dc.contributor.advisor 黃子銘zh_TW
dc.contributor.advisor Huang, Tzee-Mingen_US
dc.contributor.author (Authors) 李柏宏zh_TW
dc.contributor.author (Authors) Lee,Po- Hungen_US
dc.creator (作者) 李柏宏zh_TW
dc.creator (作者) Lee, Po- Hungen_US
dc.date (日期) 2009en_US
dc.date.accessioned 9-May-2016 11:40:08 (UTC+8)-
dc.date.available 9-May-2016 11:40:08 (UTC+8)-
dc.date.issued (上傳時間) 9-May-2016 11:40:08 (UTC+8)-
dc.identifier (Other Identifiers) G0096354020en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/94725-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 統計學系zh_TW
dc.description (描述) 96354020zh_TW
dc.description.abstract (摘要) 函數型資料分析為近年發展的統計方法。函數型資料是在一段特定時間上，我們只在離散的時間點上收集觀測值。例如:氣象觀測站所收集到的每月氣溫、雨量資料，即是一種常見的函數型資料。函數型資料主要有三種特色，共同趨勢性、觀測個體反應強度不同，觀測個體時間特色上的差異。本文研究主要是使用，Brumback與Lindstrom在2004所提出的自模型迴歸族(self-modeling)當作模型架構來處理函數型資料的趨勢性與個體反應強度。而為了處理函數型資料的時間差異性，我們在模型中加入時間轉換函數(time transformation function)，處理函數型資料的時間差異性步驟，這個過程稱為同步化。經過同步化的處理後，能幫助研究者更清楚資料的特性。模型中除了時間轉換函數的部份，其餘模型中的參數我們是利用馬可夫鏈蒙地卡羅法中的Gibbs Sampling來進行參數的抽樣，並以取出的抽樣值來估計參數。時間轉換函數的部份，我們使用概似懲罰函數(penalized likelihood function)來估計時間轉換函數的參數部份。由於函數型資料擁有趨勢性，我們預期不同類別的資料，會呈現不同的趨勢性，我們將利用此一特色當做分類上的標準。
      關鍵詞:函數型資料分析、曲線同步化、曲線區別分析、馬可夫鏈蒙地卡羅法。		zh_TW
dc.description.abstract (摘要) Functional data are random curves observed in a period of time at discrete time points.They often exhibit a common shape, but with variations in amplitude and phase across curves.To estimate the common shape,some adjustment for synchronization is often made,which is also known as time warping or curve registration.In this thesis,splines are used to model the warping functions and the common shape. Certain parameters are allowed to be random.For the estimation of the random parameters,priors are proposed so that samples from the posteriors can be obtained using Markov chain Monte Carlo methods.For the estimation of non-random parameters, a penalized likelihood approach is used. It is found via simulation studies that for a set of random curves with a common shape,the estimated common shape function looks like the true function up to a location-scale transform,and the curve alignment based on estimated time warping functions looks reasonable.For two groups of random curves which differ in the group common shape functions,synchronization also improves the discrimination between groups in some cases.
     
     Key words: functional data analysis,curve registration,curve discrimination,markov chain monte carlo method.		en_US
dc.description.tableofcontents 1 緒論 5
      1.1 研究動機……………………………………………………5
      1.2 研究目的……………………………………………………5
     2 文獻探討 7
     3 研究方法 9
      3.1 模型假設……………………………………………………9
      3.2 共同型態函數………………………………………………12
      3.3 時間轉換函數………………………………………………13
      3.4 參數估計與分類……………………………………………14
     4 資料分析 19
      4.1 模擬資料分析一……………………………………………19
      4.2 模擬資料分析二……………………………………………23
      4.3 柏克萊地區身高追蹤資料…………………………………26
     5 結論與建議 28
      5.1 結論…………………………………………………………28
      5.2 建議…………………………………………………………29		zh_TW
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0096354020en_US
dc.subject (關鍵詞) 函數型資料分析zh_TW
dc.subject (關鍵詞) 曲線同步化zh_TW
dc.subject (關鍵詞) 曲線區別分析zh_TW
dc.subject (關鍵詞) 馬可夫鏈蒙地卡羅法zh_TW
dc.subject (關鍵詞) function data analysisen_US
dc.subject (關鍵詞) curve registrationen_US
dc.subject (關鍵詞) curve discriminationen_US
dc.subject (關鍵詞) Markov chain Monte Carlo methoden_US
dc.title (題名) 貝氏曲線同步化與分類zh_TW
dc.title (題名) Bayesian Curve Registration and Classificationen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) [1] Anderson, C. W.,Stolz, E. A.,and Shamsunder, S., Multivariate autoregressive
     models for classication of spontaneous electroencephalogram during mental tasks.
     IEEE Transactions on Biomedical Engineering, 45:277{286, 1998.
     [2] Brumback, L. C.,Lindstrom, M. J., Self modeling with
     exible, random time transformations.
     Biometrics, 60(2):461{470, 2004.
     [3] Buner, F.,Biau, G.,and Wegkamp, M. H., Functional classication in hilbert spaces.
     IEEE Transactions on Information Theory, 51:2163{2172, 2005.
     [4] Deboor, C., A Practical Guide to Splines. Springer-Verlag Berlin and Heidelberg
     GmbH & Co. K, 1978.
     [5] Carroll, R. J.,Ruppert, D., Spatially-adaptive penalties for spline tting. Australian
     and New Zealand Journal of Statistics, 42:205{223, 2000.
     [6] Conan-Guez, B.,Rossi, F., Phoneme discrimination with functional multilayer perceptron.
     In D. Banks, L. House, F. R. McMorris, P. Arabie, and W. Gaul, editors,
     Classication, Clustering, and Data Mining Applications (Proceedings of IFCS
     2004), pages 157{165, Chicago, Illinois, July 2004. IFCS, Springer.
     [7] Fleet, S. L.,Glendinning, R. H., Classifying non-uniformly sampled vector-valued
     curves. Pattern Recognition, 37:1999{2008, 2004.
     [8] Gareth, M. J., Curve alignment by moment. Annals of Applied Statistics, 1:480{501,
     2007.
     [9] Gasser, T.,Kneip, A., Searching for structure in curve samples. Journal of the
     American Statistical Association, 90:1179{1188, 1995.
     [10] Gelman, A.,Rubin, D. B., Inference from iterative simulation using multiple sequences.
     Statistical Science, 7:457{511, 1992.
     [11] Geweke, J., Evaluating the accuracy of sampling-based approaches to the calculation
     of posterior moments (Disc: P189-193). In J. M. Bernardo, J. O. Berger,
     A. P. Dawid, and Smith, editors, Bayesian Statistics 4. Proceedings of the Fourth
     Valencia International Meeting, pages 169{188. Clarendon Press [Oxford University
     Press], 1992.
     [12] Heidelberger, P.,Welch, P. D., Simulation run length control in the presence of an
     initial transient. Operations Research (INFORMS), 31:1109{1144, 1983.
     [13] James, G. M.,Hastie, T. J., Functional linear discriminant analysis for irregularly
     sampled curves. Journal of the Royal Statistical Society Series B, 63:533{550, 2001.
     [14] Jank, W.,Shmueli, G., Functional data analysis in electronic commerce research.
     Statistical Science, 21(2):155{166, 2006.
     [15] Kneip, A.,Gasser, T., Convergence and consistency results for self-modeling nonlinear
     regression. The Annals of Statistics, 16:82{112, 1988.
     [16] Lang, S.,Brezger, A., Bayesian p-splines. Journal of Computational and Graphical
     Statistics, 13:183{212, 2004.
     [17] Naya, S., Cao, R., Artiaga, R., and García, A., New Method for Material Classication
     from TGA Data by Nonparametric Regression . Materials Science Forum,514{
     516:1452{1456,2006.
     [18] Ogden, R. T.,Miller, C. E.,Takezawa, K.,Ninomiya, S., Functional regression in
     crop lodging assessment with digital images. Journal of Agricultural, Biological,
     and Environmental Statistics, 7(3):389{402, 2002.
     [19] Poskitt, D.,Presnell, B.,and Hall, P., A functional data-analytic approach to signal
     discrimination. Technometrics, 23:73{102, 2001.
     [20] Ramsay, J. O.,Li, X., Curve registration. Journal of the Royal Statistical Society,
     Series B: Statistical Methodology, 60:351{363, 1998.
     [21] Rossi, F.,Conan-guez, B., Functional multi-layer perceptron: a nonlinear tool for
     functional data analysis. In Neural Networks, pages 45{60, 2005.
     [22] Rossi, F.,Villa, N., Support vector machine for functional data classication. EEG
     NEUROCOMPUTING, 69:730-742, 2006.
     [23] Silverman, B. W., Incorporating parametric effects into functional principal components
     analysis. Journal of the Royal Statistical Society, Series B: Methodological,
     57:673{689, 1995.
     [24] Silverman, B. W.,Ramsay, J. O., Functional Data Analysis. Berlin:Springer-Verlag,
     1997.
     [25] Silverman, B. W.,Ramsay, J. O., Applied Functional Data Analysis:Methods and
     Case Studies. Berlin:Springer-Verlag, 2002.
     [26] Wang, X.,Rossi, N.,Ramsay, J. O., Nonparametric item response function estimates
     with the EM algorithm. J. Educational and Behavioral Statistics, 27:291{317, 2002.		zh_TW