Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/97325
DC FieldValueLanguage
dc.contributor陳鵬文zh_TW
dc.contributorPeng-Wen Chenen_US
dc.contributor.author蘇郁舜zh_TW
dc.contributor.authorYu-Shun Suen_US
dc.contributor.other應用數學系所zh_TW
dc.date2018zh_TW
dc.date.accessioned2019-02-01T05:32:36Z-
dc.identifier.citation[1] Robert J. Mason, MD, V. Courtney Broaddus, MD, Thomas Martin, Talmadge King, Jr., MD, Dean MD Schraufnagel, John F. Murray, MD, DSc(Hon), FRCP and Jay A. Nadel, MD, DSc(HON) “Murray and Nadel’s textbook of respiratory medicine.”Chapter 38. ISBN 1-4160-4710-7. [2] Xin Liu, Duygu Tosun, Michael W Weiner, Norbert Schuff,“Locally linear embedding (LLE) for MRI based Alzheimer’s disease classification”, Published 2013 in NeuroImage. [3] Ardeshir Mohammad Ebtehaj, Rafael Luis Bras, Efi Foufoula-Georgiou, “Shrunken Locally Linear Embedding for Passive Microwave Retrieval of Precipitation ”, Submitted on 2 May 2014 (v1), last revised 6 Sep 2014 (this version, v2). [4] Pearson, K. (1901). “On Lines and Planes of Closest Fit to Systems of Points in Space”. Philosophical Magazine 2 (11): 559–572. [5] Hotelling, H. (1933).“Analysis of a complex of statistical variables into principal components.”Journal of Educational Psychology. [6] https://en.wikipedia.org/wiki/Principal_ component_ analysis [7] http://justdark.github.io/博客/2016/11/12/pca_ svd_ recall/ [8] S. T. Roweis and L. K. Saul, “Nonlinear Dimensionality Reduction by Locally Linear Embedding”, Science Vol 290, 22 December 2000, 2323–2326. [9] Chun-An Chen, “Dimension reduction on analysis asthma lung deformation”,January 2016. [10] S. T. Roweis and L. K. Saul, “An Introduction to Locally Linear Embedding”,January 2001. [11] S. T. Roweis and L. K. Saul, “An Introduction to Locally Linear Embedding”, https://www.cs.nyu.edu/ roweis/lle/,January 2001 [12] Kilian Q. Weinberger and Lawrence K. Saul,“Unsupervised Learning of Image Manifolds by Semidefinite Progranning”, International Journal of Computer Vision 70(1),77-90,2006.zh_TW
dc.identifier.urihttp://hdl.handle.net/11455/97325-
dc.description.abstract資料降維化不僅讓我們壓縮數據而使用較少的計算機內存磁碟空間, 也讓我們加快學習算法。最重要的是,降維可以幫助我們能將數據可視化, 我們便能尋找到數據的低維架構及其中所隱含的重要資訊。 在所有的數據可視化技術中,Principal components analysis(PCA) 是揭示線性結構中最常用的方法,Maximum variance unfolding(MVU) 和Locally linear embedding(LLE) 則是非線性結構降維最典型的方法。在本文中,我們對MVU和LLE 的鄰近點選取概念應用使用在交替方向乘子法(The alternating direction method of multipliers,簡稱ADMM) 中,並透過最大化資料點的F-norm 來達到降維的效果。 透過代入LLE 的輸出作為ADMM 迭代初始值,可以用來改善LLE 降維後會扭曲變形的問題,讓降維的結果達到更好的效果。 另外,我們做出了一系列的實驗足以證明他們的性能,包含swissroll 和自製九維模型,以及探討如何選擇較好的ADMM演算法參數β。zh_TW
dc.description.abstractDimensionality reduction helps us not only reduce the use of capacity of computer disk, but also speed up the machine learning algorithms. Most importantly, dimensionality reduction helps us visualize the data so that we can find the structure in low rank structure and the underlying information lurking behind it. Among all the data visualization techniques, Principle Component Analysis(PCA) is the most popular method in uncovering the linear low rank structure. Maximum Variance Unfolding(MVU) and Locally Linear Embedding(LLE) are the classical methods for dimensionality reduction of nonlinear structures. In this paper, we use the concept of neighbor selection of MVU and LLE in the Alternating Direction method of Multipliers(ADMM) and accomplish dimensionality reduction by maximizing Frobenius norm of the data. The output of LLE can be used as an initial value of ADMM iteration to improve the result of distortion and lost distant by LLE to get a better result. In addition, we make a series of experiments to demonstrate their performance, including swissroll and nine-dimensional models, as well as exploring how to choose the better parameters beta of ADMM algorithm.en_US
dc.description.tableofcontents誌謝辭i 中文摘要ii Abstract iii 壹、Introduction 1 一、背景和動機. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 二、論文主要貢獻. . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 三、論文架構. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 貳、Lung preprocessing 3 一、Lung description . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 二、Digital Lung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 三、Data processing of Lung . . . . . . . . . . . . . . . . . . . . . . 5 參、Linear dimensionality reduction and nonlinear dimensionality reduction 7 一、Principal Component Analysis (PCA) . . . . . . . . . . . . . . . 7 二、Locally Linear Embedding (LLE) . . . . . . . . . . . . . . . . . 9 三、Simulation of swissroll . . . . . . . . . . . . . . . . . . . . . . . . 12 四、Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 肆、The alternating direction method of multipliers 17 一、Alternating direction method for matrix . . . . . . . . . . . . . . 17 二、Alternating direction method for vector . . . . . . . . . . . . . . 19 三、矩陣ADMM 與向量ADMM 的還原比較. . . . . . . . . . . . . 21 1、資料量n 與條件數量N 的比值. . . . . . . . . . . . . . . 21 2、效能比較. . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3、總結. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 伍、Dimensionality reduction by Alternating direction method 23 一、鄰近點量測限制. . . . . . . . . . . . . . . . . . . . . . . . . . . 23 二、最大化X 的Frobenius norm . . . . . . . . . . . . . . . . . . . . 25 1、矩陣ADMM 降維. . . . . . . . . . . . . . . . . . . . . . 25 2、矩陣ADMM 在swissroll 實驗模擬. . . . . . . . . . . . . 27 3、向量ADMM 降維. . . . . . . . . . . . . . . . . . . . . . 28 4、向量ADMM 在swissroll 實驗模擬. . . . . . . . . . . . . 31 陸、向量ADMM 的初始值和參數32 一、2D swissroll 降維. . . . . . . . . . . . . . . . . . . . . . . . . . 32 二、3D swissroll 降維. . . . . . . . . . . . . . . . . . . . . . . . . . 32 三、參數β的選擇. . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 1、ADMM 降維法與參數β的關係. . . . . . . . . . . . . . . 36 2、向量ADMM 的參數Beta 預測. . . . . . . . . . . . . . . 36 3、參數Beta 與c 和Optimal rate 的關係. . . . . . . . . . . 37 4、 β預測值與實驗最佳 β的關係. . . . . . . . . . . . . . . 38 柒、Comparison of Different Methods on High dimensionality reduction 40 一、動機和目的. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 二、資料設計. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 三、降維方法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 1、PCA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2、矩陣ADMM . . . . . . . . . . . . . . . . . . . . . . . . . 42 3、LLE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4、向量ADMM 以隨機矩陣作為初始值. . . . . . . . . . . . 43 5、向量ADMM 以LLE 的降維結果作為初始值. . . . . . . 44 捌、結論45 補充實驗46 貳-四、Maximum Variance Unfolding(MVU) . . . . . . . . . . . . . . 46 肆-四、相鄰矩陣Adjecency Matrix . . . . . . . . . . . . . . . . . . . 48 1. 固定維度,在不同n 以及N 還原的結果. . . . . . . . . . 48 總結. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 肆-五、加入雜訊的影響. . . . . . . . . . . . . . . . . . . . . . . . . 50 1、維度r 等於2 . . . . . . . . . . . . . . . . . . . . . . . . . 50 2、維度r 等於3 . . . . . . . . . . . . . . . . . . . . . . . . . 51 3、固定N 與n 的比例為7,比較不同維度還原誤差結果. . 51 4、總結. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 伍-四-2、Beta 值與ADMM 的關係. . . . . . . . . . . . . . . . . . . 52 參考文獻53zh_TW
dc.language.isozh_TWzh_TW
dc.rights同意授權瀏覽/列印電子全文服務,2018-01-31起公開。zh_TW
dc.subject可視化技術zh_TW
dc.subjectPrincipal components analysis(PCA)zh_TW
dc.subjectLocally linear embedding(LLE)zh_TW
dc.subjectMaximum variance unfolding(MVU)zh_TW
dc.subject交替方向乘子法(ADMM)zh_TW
dc.subjectVisualization techniquesen_US
dc.subjectPrinciple Component Analysis(PCA)en_US
dc.subjectLocally Linear Embedding(LLE)en_US
dc.subjectMaximum Variance Unfolding(MVU)en_US
dc.subjectAlternating Direction method of Multipliers(ADMM)en_US
dc.title交替方向乘子法在降維問題之應用zh_TW
dc.titleApplication of Alternating Direction of Multiplier Method on dimensional reductionen_US
dc.typethesis and dissertationen_US
dc.date.paperformatopenaccess2018-01-31zh_TW
dc.date.openaccess2018-01-31-
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item.openairetypethesis and dissertation-
item.cerifentitytypePublications-
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