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研究生：	張元綺 Yuan-Chi Chang
論文名稱：	Bayesian method for sparse principal component analysis
指導教授：	王紹宣 Shao-Hsuan Wang
口試委員:
學位類別：	碩士 Master
系所名稱：	理學院 - 統計研究所 Graduate Institute of Statistics
論文出版年：	2022
畢業學年度：	110
語文別：	英文
論文頁數：	37
中文關鍵詞：	全部局部收縮先驗、主成分分析、載荷係數、稀疏性
外文關鍵詞：	global-local shrinkage prior, loadings, SPCA
相關次數：	點閱：21 下載：0
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主成分分析(PCA)是一種常見且熱門的降維方法。然而，當我們想通過主成分的載荷係數(loading)進一步對資料與變數之間做推論時，常因載荷係數不為零而難以得到簡易的解釋結果。本文的主要目的是嘗試透過貝氏方法得到 SPCA 標準下的稀疏載荷，其中我們使用一種全部局部收縮先驗(global-local shrinkage prior)模型 MBSP-TPBN。數值模擬和實際數據證明本文提出的方法。

Principal component analysis (PCA) is a common and popular dimensionality reduc- tion method. However, when we want to make further inferences between data and variables through the loadings of principal components, it is often difficult to obtain simple interpretation results due to all non-zero loadings. The main purpose of this thesis is to try to obtain the sparse loadings under the SPCA criterion based on a Bayesian approach, in which we use a global-local shrinkage prior model MBSP-TPBN. The numerical study and real data demonstrate the proposed method in the article.

1 Introduction 1
2 Literature Review 3
   2.1 SparsePrincipalComponentAnalysis .................... 3 
         2.1.1 Sparse Principal Component Analysis Criterion . . . . . . . . . . 4 
         2.1.2 AdjustedTotalVariance ........................ 5
   2.2 Global-localShrinkagePriors ......................... 6
         2.2.1 Multivariate Bayesian Model with Shrinkage Priors . . . . . . . . 7
         2.2.2 Three-ParameterBetaNormalFamily ................ 8
         2.2.3 TheMBSP-TPBNModel........................ 9
   2.3 TheGibbsSampling .............................. 10
         2.3.1 The Conditional Distributions of the MBSP-TPBN Model . . . . . 10
3 Proposed Methodology 12
   3.1 BayesianMethodforSparsePrincipalComponent . . . . . . . . . . . . . 12 
         3.1.1 Sparse Principal Component Analysis via the MBSP-TPBN Model 12
4 Numerical Study 15
   4.1 Case1.Gaussiandistribution ......................... 16 
   4.2 Case2.Uniformdistribution ......................... 18
5 Application 20
   5.1 Glassdata .................................... 20 iv
   5.2 SyntheticControlChartTimeSeriesData .................. 22
6 Conclusion 25
Reference 27
                                

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