兩種不同 ALTERNATING DIFFUSION 方法的驗證｜國立清華大學博碩士論文庫

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研究生：	汪海宇 Wang, Hai-Yu.
論文名稱：	兩種不同 ALTERNATING DIFFUSION 方法的驗證 VALIDATION ON TWO DIFFERENT ALTERNATING DIFFUSION METHODS
指導教授：	許元春 Sheu, Yuan-Chung 鄭志豪 Teh, Jyh-Haur
口試委員:	劉聚仁 Liu, Gi-Ren 洪芷漪 Hong, Jyy-I
學位類別：	碩士 Master
系所名稱：	理學院 - 數學系 Department of Mathematics
論文出版年：	2019
畢業學年度：	108
語文別：	英文
論文頁數：	38
中文關鍵詞：	交互擴散、擴散映射、降維度、共變數、睡眠階段
外文關鍵詞：	alternating diffusion, diffusion map, dimensionality reduction, common vairable, sleep stage
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交互擴散映射(Alternating diffusion map)是一種降維(dimension reduction)方法。對同一現象同時具有數個觀測資料時，可用於整合並從中抽取出資料特徵。Lederman, Talmon, Wu, Lo and Coifman提出一種交互擴散映射過程用於找出共同來源(common sources)的距離關係。Shnitzer, Ben-Chen, Guibas, Talmon and Wu基於交互擴散映射引入了兩個算子，可用於分辨資料的相同與相異結構。本文的目的是驗證兩種交互擴散映射方法，並比較兩方法在睡眠階段分類中的績效。此外，我們也針對Lederman等人提出的交互擴散映射過程給出離散版本證明。

Alternating diffusion map is a dimension reduction method which is used to integrate and extract features of the observations measured from multiple sensors. Lederman, Talmon, Wu, Lo and Coifman [1] proposed a process to find out a distance relation of common sources. Shnitzer, Ben-Chen, Guibas, Talmon and Wu [2] introduced two operator based on alternating diffusion method to distinguish common and difference structure of the datasets. The goal of this paper is to validate two alternating diffusion methods and compare the performance of two different alternating diffusion method on sleep stage assessment. In addition, we give a proof of discrete version for alternating diffusion process proposed by Lederman et. al.

Table of Contents
   Preliminary    1
1    Kronecker Product    1
2    Lederman’s method    1
3    Shnitzer’s method    5
   Discrete version of Lederman’s method    8
   Validation    14
1    Validation on Lederman’s method    14
2    Validation on Shnitzer’s method    16
   Sleep Stage Assessment    18
1    Feature extraction through Lederman’s method    20
2    Feature extraction through Shnitzer’s method    22
3    Cluster based on density of eigenvectors    24
4    Regrouped by subjects    25
   Conclusion    28
   Algorithm    29
References    38


                                

[1] Lederman, Roy R., Ronen Talmon, Hau-Tieng Wu, Yu-Lun Lo, and Ronald R. Coifman.
"Alternating Diffusion for Common Manifold Learning with Application to Sleep Stage Assessment."
2015 IEEE International Conference on Acoustics, Speech and Signal Processing
(ICASSP), 2015. doi:10.1109/icassp.2015.7179075.
[2] Shnitzer, T., Ben-Chen, M., Guibas, L., Talmon, R., andWu, H. T. "Recovering hidden components
in multimodal data with composite diffusion operators." arXiv preprint arXiv:1808.07312
[3] Coifman, Ronald R., and Stéphane Lafon. "Diffusion Maps." Applied and Computational
Harmonic Analysis 21, no. 1 (2006): 5-30. doi:10.1016/j.acha.2006.04.006.
[4] Froyland, Gary. "Dynamic Isoperimetry and the Geometry of Lagrangian Coherent Structures."
Nonlinearity 28, no. 10 (2015): 3587-622. doi:10.1088/0951-7715/28/10/3587.
[5] Froyland, Gary, and Eric Kwok. "A Dynamic Laplacian for Identifying Lagrangian Coherent
Structures on Weighted Riemannian Manifolds." Journal of Nonlinear Science, 2017.
doi:10.1007/s00332-017-9397-y.

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