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研究生:黃駿麒
研究生(外文):Chon-Kei Wong
論文名稱:偏最小平方迴歸在光阻劑資料上的應用
論文名稱(外文):Applications of partial least squares regression on photoresist data
指導教授:蔡志群
指導教授(外文):Chih-Chun Tsai
口試委員:林千代彭健育蔡志群
口試委員(外文):Chien-Tai LinChien-Yu PengChih-Chun Tsai
口試日期:2020-06-30
學位類別:碩士
校院名稱:淡江大學
系所名稱:數學學系數學與數據科學碩士班
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2020
畢業學年度:108
語文別:中文
論文頁數:25
中文關鍵詞:偏最小平方迴歸SIMPLS
外文關鍵詞:partial least squares regressionSIMPLS
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  • 點閱點閱:105
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半導體在我們生活中到處都會用到,在晶圓生產過程的蝕刻製程中需要用到光阻劑,本研究對一光阻劑資料進行分析,對配方變數及成品變數進行迴歸建模。配方變數及成品變數都有共線性的問題,對於這種情況,偏最小平方迴歸就是其中一個進行建模的方法。本研究介紹偏最小平方迴歸的原理及其演算法,對光阻劑資料進行建模,且預測新配方的成品變數。最後,本文將給定成品規格,反求得最佳配方設計。
Semiconductor are used everywhere in our daily life, such as mobile phones, computers, smart home appliances. In wafer manufacturing process, photoresist is used to etch the circuitry pattern on wafers. In this study, motivated by photoresist data. First, we constructed the regression model between the recipe variable and the specification variable. Then, given new recipe variable, the specification variable can be predicted. Finally, given specification target, the optimal solution on recipe variable can be obtained.
1 緒論 1
1.1 前言 1
1.2 文獻探討 3
1.3 研究動機與目的 5
1.4 研究架構 10
2 偏最小平方迴歸分析 11
2.1 主成份分析 11
2.2 偏最小平方迴歸分析 13
2.3 參數估計演算法 14
3 實例分析 17
3.1 實例資料分析 17
4 結論 23
參考文獻 24
[1]H. Abdi (2010). “Partial least squares regression and projection on latent structure regression (PLS Regression),” WIREs Computational Statistics, Vol. 2, 97-106.
[2]H. Abdi, W. W. Chin, V. Esposito Vinzi, G. Rusolillo & L. Trinchera (2013). New Perspectives in Partial Least Squares and Related Methods. Springer.
[3]A. L. Boulesteix & K. Strimmer (2007). “Partial least squares: A versatile tool for the analysis of high-dimensional genomic data,” Briefings in Bioinformatics, Vol. 8, 32–44.
[4]S. de Jong (1993). “SIMPLS: an alternative approach to partial least squares regression,” Chemometrics and Intelligent Laboratory Systems, Vol. 18, 251-263.
[5]K. Faber & B. R. Kowalski (1997). “Propagation of measurement errors for the validation of predictions obtained by principal component regression and partial least squares,” Journal of Chemometrics, Vol. 11, 181-238.
[6]A. Höskuldsson (1988). “PLS regression methods,” Journal of Chemometrics, Vol. 2, 211-228.
[7]A. Lorber & B. R. Kowalski (1988). “A note on the use of the partial least-squares method for multivariate calibration,” Applied Spectroscopy, Vol. 42, 1572-1574.
[8]R. Manne (1987). “Analysis of two partial-least-squares algorithms for multivariate calibration,” Chemometrics and Intelligent Laboratory Systems, Vol. 2, 187-197.
[9]K. Pearson (1901). “On lines and planes of closest fit to systems of points in space,” Philosophical Magazine, Vol. 2, 559-572.
[10]R. Rosipal & N. Krämer (2005). “Overview and recent advances in partial least squares,” Lecture Notes in Computer Science, Vol. 3940, 34-51.

[11]L. I. Smith (2002). A tutorial on principal components analysis, http://www.cs.otago.ac.nz/cosc453/student_tutorials/principal_components.pdf .
[12]S. Wold, A. Ruhe, H. Wold & W. J. Dunn (1982). “The collinearity problem in linear regression. The partial least squares (PLS) approach to generalized inverses,” SIAM Journal on Scientific and Statistical Computing, Vol. 5, 735-743.
[13]X. Q. Zeng & G. Z. Li (2014). “Incremental partial least squares analysis of big streaming data,” Pattern Recognition, Vol. 47, 3726-3735.
[14]張珮甄 (2012). “PLS2 algorithms comparison on compositional data,”國立高雄大學統計學研究所碩士班論文.
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