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| Title: | 無母數迴歸偵測峰谷位置
An Approach for Peak-Valley Detection in Nonparametric Regression Estimation |
| Authors: | 吳承臻
Wu, Chen-Jen |
| Contributors: | 黃子銘
HUANG, ZI-MING
吳承臻
Wu, Chen-Jen |
| Keywords: | 無母數迴歸
保序迴歸
樣條函數
節點選取
峰值位置偵測
Nonparametric Regression
Isotonic Regression
B-spline
Knots Selection
Peak Detection |
| Date: | 2022 |
| Issue Date: | 2022-08-01 17:16:19 (UTC+8) |
| Abstract: | 偵測曲線峰谷位置是個常見問題，本論文中提出一種偵測方法作為部分節點選取方式，先透過統計檢定方法初步抓取峰谷位置，再利用保序迴歸(isotonic regression)計算殘差平方和評估偵測位置的優劣並進行優化改善偵測點。最後再使用樣條函數配適曲線。
在週期函數的資料下，表現會比其他偵測峰谷演算法來配適樣條函數表現來得好，
但是根據不同參數設置下，在模擬試驗有發現可能漏抓峰谷點的情況，其配適結果明顯能看出有異，而此情況在震盪幅度或週期不一的峰谷資料下更常出現，所以未來可以繼續在演算法上面做改進。
Peak and valley detection is a common problem, we propose a peak-finding method as a selection approach for some konts. In this study, we first finds peaks and valleys locations roughly via hypothesis test, then optimizes the locations
more precisely by minimizing the RSS of Isotonic regression.Finally, fit the curve by b-spline function.
The performance of our study is better than others
peak-finding method in periodic data. But according to
different combination of argument, there are some situations
that some peaks or valleys are not detected in simulation,
and this kind of mischance are much common in complicated
amplitude or non-periodic data. |
| Reference: | [1] Geert Brouwer and J A J Jansen. Deconvolution method for identification of peaks in digitized spectra. Analytical Chemistry, 45(13), 1973-11-01.
[2] Norman Allen Dyson and Roger M Smith. Chromatographic integration methods, volume 3. Royal Society of Chemistry, 1998.
[3] Herbert Edelsbrunner and John L Harer. Computational topology: an introduction. American Mathematical Society, 2022.
[4] JL Excoffier and G Guiochon. Automatic peak detection in chromatography. Chromatographia, 15(9):543–545, 1982.
[5] Fuchang Gao and Lixing Han. Implementing the nelder-mead simplex algorithm with adaptive parameters. Computational optimization and applications., 51(1), 2012-1.
[6] Donald Goldfarb and Ashok Idnani. A numerically stable dual method for solving strictly convex quadratic programs. Mathematical programming, 27(1):1–33, 1983.
[7] I J Schoenberg. Contributions to the problem of approximation of equidistant data by analytic functions. part b. on the problem of osculatory interpolation. a second class of analytic approximation formulae. Quarterly of applied mathematics., 4(2), 1946-01-01.
[8] Larry L. Schumaker. Spline functions : basic theory / Larry L. Schumaker. Cambridge Core. Cambridge University Press, Cambridge, third edition. edition, 2007.
[9] Quentin F Stout. Unimodal regression via prefix isotonic regression. Computational Statistics & Data Analysis, 53(2):289–297, 2008.
[10] 王姿尹. 兩種基於 b-spline 迴歸模型之節點選取演算法比較, 2019.
[11] 賴品霖. 比較使用 kernel 和 spline 法的傘型迴歸估計, 2016. |
| Description: | 碩士
國立政治大學
統計學系
109354018 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0109354018 |
| Data Type: | thesis |
| DOI: | 10.6814/NCCU202200932 |
| Appears in Collections: | [統計學系] 學位論文
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| 401801.pdf | | 5666Kb | Adobe PDF2 | 78 | View/Open |
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