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| Title: | 動差對齊法之研究
A study of moment-based registration method |
| Authors: | 蕭詠勳
Hsiao, Yung Hsun |
| Contributors: | 黃子銘
蕭詠勳
Hsiao, Yung Hsun |
| Keywords: | 動差
對齊
函數型資料分析
moment
alignment
functional data analysis |
| Date: | 2012 |
| Issue Date: | 2013-06-03 18:14:59 (UTC+8) |
| Abstract: | 函數型資料分析都會面對到時間變異性的問題，而在處理時間變異性的方法上，
最初有利用類似地標概念的landmark registration以及利用連續型單調時間轉換函數的continuous monotone registration，此兩方法分別給予函數上某些點的特徵與函數大致的外型做為時間對齊時的條件，假使函數在特徵或是外型上並不明確，則在對齊的效果就會不盡理想，而針對這個問題James在2007年提出了curve alignment by moments，同時給予函數特徵與外型作為時間對齊之條件，而定義函數特徵則是透過特徵函數與動差，特徵函數會根據函數本身的特性自動反映函數特徵，本研究針對函數某特徵不唯一時會導致動差在反映函數特徵發生誤差，將特徵函數進行分段，使函數在定義特徵時較不受到函數特徵重複的影響，另外本研究也就參數估計的過程將原本同時求取函數外型與時間轉換函數參數的部分，修正為先給定函數外型參數求取時間轉換函數參數，再將求出的時間轉換函數參數固定求出新的外型函數參數，減少參數估計需要消耗的時間。
In functional data analysis, it is common that the data curves exhibit roughly the same structure with some variation in time. In order to estimate the common structure, it is necessary to align the curves.
Early alignment approaches include landmark registration and continuous monotone registration. In landmark registration, curves are aligned by matching certain curve characters. In continuous monotone registration, curves are aligned by matching their shapes. James (2007) proposed an alignment method called curve alignment by moments (CAM). In the CAM approach, curves are aligned by matching both their shapes and moments, where curve moments may be chosen to reflect certain curve characters. The CAM approach is flexible, but the computation is time consuming.
In this thesis, two modified versions of CAM are proposed based on a model assuming the curves are of the same shape. An algorithm is proposed to find the warping functions and the shape function iteratively. In the two modified versions,
the number of parameters involved in the computation is largely reduced. Another modification considered in this thesis is to use moments based on pieces of curves instead of the whole curves. The advantage of using the modified
moments is so that repeated characters in each curve may be identified. Simulation results indicate that such modification can lead to substantial improvement in certain cases. |
| Reference: | [1] de Boor C. A Practical Guide to Splines. Springer-Verlag, 1st edition edition,1978.
[2] Ferraty F. and Vieu P. Curves discrimination : a nonparametric functional approach. Computational Statistics and Data Analysis, 44:161–173, 2003.
[3] James G. M.. Curve alignment by moments. Annals of Applied Statistics, 1:480–501, 2007.
[4] James G. M., Hastie T., and Sugar C. Principal component models for sparse functional data. Biometrika, 87:587–602, 2000.
[5] Ramsay J. O. and Li X. Curve registration. Journal of the Royal Statistical Society, B. 60:351–363, 1998.
[6] Ramsay J. O. and Silverman B. W. Functional Data Analysis. Springer, New York, 1997.
[7] Sangalli L. M., Secchi P., Vantini S., and Vitelli V. k-mean alignment for curve clustering. Computational Statistics and Data Analysis, 54:1219–1233, 2008.
[8] Silverman B. W. and Ramsay J. O. Applied Functional Data Analysis : Methods and Case Studies. Springer-Verlag, 2002. |
| Description: | 碩士
國立政治大學
統計研究所
99354019
101 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0993540191 |
| Data Type: | thesis |
| Appears in Collections: | [統計學系] 學位論文
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