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題名 無母數迴歸偵測峰谷位置
An Approach for Peak-Valley Detection in Nonparametric Regression Estimation
作者 吳承臻
Wu, Chen-Jen
貢獻者 黃子銘
HUANG, ZI-MING
吳承臻
Wu, Chen-Jen
關鍵詞 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
日期 2022
上傳時間 1-八月-2022 17:16:19 (UTC+8)
摘要 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.
參考文獻 [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.
描述 碩士
國立政治大學
統計學系
109354018
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0109354018
資料類型 thesis
dc.contributor.advisor 黃子銘zh_TW
dc.contributor.advisor HUANG, ZI-MINGen_US
dc.contributor.author (作者) 吳承臻zh_TW
dc.contributor.author (作者) Wu, Chen-Jenen_US
dc.creator (作者) 吳承臻zh_TW
dc.creator (作者) Wu, Chen-Jenen_US
dc.date (日期) 2022en_US
dc.date.accessioned 1-八月-2022 17:16:19 (UTC+8)-
dc.date.available 1-八月-2022 17:16:19 (UTC+8)-
dc.date.issued (上傳時間) 1-八月-2022 17:16:19 (UTC+8)-
dc.identifier (其他 識別碼) G0109354018en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/141010-
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) 109354018zh_TW
dc.description.abstract (摘要) 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。		zh_TW
dc.description.abstract (摘要) 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.		en_US
dc.description.tableofcontents 致謝 ii
中文摘要 iii
Abstract iv
目錄 v
表目錄 vii
圖目錄 viii
第一章 緒論 1
第二章 文獻回顧 2
第一節 樣條函數文獻回顧 2
第二節 傘型限制文獻探討 3
第三節 峰值檢測文獻探討 4
一、Matched Filters 4
二、由導數偵測峰值 4
三、現有函式庫作法 5
第三章 研究方法 8
第一節 統計檢定 8
第二節 檢定配適範圍選取 10
第三節 偵測峰、谷算法 11
一、自動偵測峰值所需配適範圍 11
二、自動偵測峰值座標 12
第四節 峰、谷位置優化 13
第五節 建立 B-Splines 函數估計 14
第四章 模擬資料分析 16
第一節 驗證檢定方法的可行性 16
第二節 以簡單週期性資料為例 18
一、模擬結果 19
二、峰谷偵測方法比較 21
第五章 結論與建議 22
第一節 研究結論 22
第二節 研究建議 22
附錄 A 24
A.1 程式碼 24
A.2 以週期不一資料為例 24
參考文獻 26		zh_TW
dc.format.extent 5802378 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0109354018en_US
dc.subject (關鍵詞) 無母數迴歸zh_TW
dc.subject (關鍵詞) 保序迴歸zh_TW
dc.subject (關鍵詞) 樣條函數zh_TW
dc.subject (關鍵詞) 節點選取zh_TW
dc.subject (關鍵詞) 峰值位置偵測zh_TW
dc.subject (關鍵詞) Nonparametric Regressionen_US
dc.subject (關鍵詞) Isotonic Regressionen_US
dc.subject (關鍵詞) B-splineen_US
dc.subject (關鍵詞) Knots Selectionen_US
dc.subject (關鍵詞) Peak Detectionen_US
dc.title (題名) 無母數迴歸偵測峰谷位置zh_TW
dc.title (題名) An Approach for Peak-Valley Detection in Nonparametric Regression Estimationen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) [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.		zh_TW
dc.identifier.doi (DOI) 10.6814/NCCU202200932en_US