| dc.contributor.advisor | 黃子銘 | zh_TW |
| dc.contributor.advisor | HUANG, ZI-MING | en_US |
| dc.contributor.author (Authors) | 吳承臻 | zh_TW |
| dc.contributor.author (Authors) | Wu, Chen-Jen | en_US |
| dc.creator (作者) | 吳承臻 | zh_TW |
| dc.creator (作者) | Wu, Chen-Jen | en_US |
| dc.date (日期) | 2022 | en_US |
| dc.date.accessioned | 1-Aug-2022 17:16:19 (UTC+8) | - |
| dc.date.available | 1-Aug-2022 17:16:19 (UTC+8) | - |
| dc.date.issued (上傳時間) | 1-Aug-2022 17:16:19 (UTC+8) | - |
| dc.identifier (Other Identifiers) | G0109354018 | en_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) | 109354018 | zh_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 locationsmore precisely by minimizing the RSS of Isotonic regression.Finally, fit the curve by b-spline function.The performance of our study is better than otherspeak-finding method in periodic data. But according todifferent combination of argument, there are some situationsthat some peaks or valleys are not detected in simulation,and this kind of mischance are much common in complicatedamplitude or non-periodic data. | en_US |
| dc.description.tableofcontents | 致謝 ii中文摘要 iiiAbstract 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 24A.1 程式碼 24A.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/#G0109354018 | en_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 Regression | en_US |
| dc.subject (關鍵詞) | Isotonic Regression | en_US |
| dc.subject (關鍵詞) | B-spline | en_US |
| dc.subject (關鍵詞) | Knots Selection | en_US |
| dc.subject (關鍵詞) | Peak Detection | en_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 Estimation | en_US |
| dc.type (資料類型) | thesis | en_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/NCCU202200932 | en_US |
