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| Title: | B-Splines不同節點選擇方法之比較
The comparison between different methods of knots selection for B-Splines |
| Authors: | 胡子卿
Hu, Zi-Qing |
| Contributors: | 黃子銘
Huang, Tzee-Ming
胡子卿
Hu, Zi-Qing |
| Keywords: | 弧線函數
節點
估計
Spline
Knots
Estimation |
| Date: | 2017 |
| Issue Date: | 2017-07-11 11:26:14 (UTC+8) |
| Abstract: | 本文以 B-Spline 的框架研究比較兩種不同的節點估計方法。第一種方法是通過最優化特定 的目標函數並結合相對應的選擇標準選擇出最優化的節點組合。第二種方法則基於幾何控制多 邊形的特性將內部節點的選擇過程與幾何圖形聯繫起來,省去了最優化的過程。另外,本文採 用『節點估計時間』與『誤差平方和』(Mean Squared Error)來評價兩種方法的估計結果。通 過分析各種不同模擬數據下兩種方法的表現情況,本文的主要發現是:第一,無論哪種資料, 第二種方法在計算速度上都是大幅領先第一種方法。第二,在數據資料較小的情況下,第一種 方法中由 Lindstrom 提出的算法並不能很好的配飾模型,最後的估計誤差較大。而在數據資料 較多的情形下,誤差與其他方法較為接近。第三,第一種方法中沒有懲罰項的算法在所有驗證 過的數據中,其表現是所有方法中最穩定且估計誤差最小的。這些發現為如何選擇恰當的節點 估計方法提供了很具價值的參考信息
This study compares two different methods of knot selection for B-Spline. The first one chooses the best knots through optimizing specific objective functions and corresponding crite- rion. Based on some properties of geometric control polygon, the second one connects the knot selection process with geometric figures, which avoids the tedious optimization. On the other hand, we use the time for estimation and the mean squared error to evaluate the performance of these two methods. There are three main findings of this study. The first finding is that the calculation speed of second method is much higher than that of the first one. Secondly, the algorithm proposed by Lindstrom in the first method is not stable and its estimation error is larger when the sample size is small. On the contrary, the performance of the algorithm proposed by Lindstrom becomes better as the sample size increases. Thirdly, the performance of the algorithm without penalty term in the first method is always better than the second method. |
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| Description: | 碩士
國立政治大學
統計學系
104354033 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0104354033 |
| Data Type: | thesis |
| Appears in Collections: | [統計學系] 學位論文
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