博碩士論文 109225025 詳細資訊




以作者查詢圖書館館藏 以作者查詢臺灣博碩士 以作者查詢全國書目 勘誤回報 、線上人數:15 、訪客IP:34.239.154.201
姓名 張元綺(Yuan-Chi Chang)  查詢紙本館藏   畢業系所 統計研究所
論文名稱
(Bayesian method for sparse principal component analysis)
相關論文
★ 長期追蹤資料上的 Gamma-EM 分群★ Contrastive Principal Component Analysis for High Dimension, Low Sample Size Data
★ Sparse Bayesian Estimation with High-dimensional Binary Response Data★ Q學習結合監督式學習在股票市場的應用
★ γ-EM approach to latent orientations for cryo-electron microscopy image clustering analysis★ Contrastive Principal Component Analysis for High-Dimension, Low-Sample-Size Data with Noise-Reduction
★ 基於Q-learning與非監督式學習之交易策略★ 視覺化股票市場之狀態變動
★ Principal Components on t-SNE
檔案 [Endnote RIS 格式]    [Bibtex 格式]    [相關文章]   [文章引用]   [完整記錄]   [館藏目錄]   [檢視]  [下載]
  1. 本電子論文使用權限為同意立即開放。
  2. 已達開放權限電子全文僅授權使用者為學術研究之目的,進行個人非營利性質之檢索、閱讀、列印。
  3. 請遵守中華民國著作權法之相關規定,切勿任意重製、散佈、改作、轉貼、播送,以免觸法。

摘要(中) 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。
摘要(英) 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.
關鍵字(中) ★ 全部局部收縮先驗
★ 主成分分析
★ 載荷係數
★ 稀疏性
關鍵字(英) ★ global-local shrinkage prior
★ principal component analysis
★ loadings
★ SPCA
★ sparse
論文目次 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
參考文獻 [1] I. T. Jolliffe. Principal Component Analysis. Berlin; New York: Springer-Verlag, 1986.
[2] Hui Zou, Trevor Hastie, and Robert Tibshirani. “Sparse principal component analysis”. In: Journal of computational and graphical statistics 15.2 (2006), pp. 265– 286.
[3] Ian T Jolliffe, Nickolay T Trendafilov, and Mudassir Uddin. “A modified princi- pal component technique based on the LASSO”. In: Journal of computational and Graphical Statistics 12.3 (2003), pp. 531–547.
[4] Sam Roweis. “EM algorithms for PCA and SPCA”. In: Advances in neural infor- mation processing systems 10 (1997).
[5] Michael E Tipping and Christopher M Bishop. “Probabilistic principal compo- nent analysis”. In: Journal of the Royal Statistical Society: Series B (Statistical Method- ology) 61.3 (1999), pp. 611–622.
[6] Cédric Archambeau and Francis Bach. “Sparse probabilistic projections”. In: Ad- vances in neural information processing systems 21 (2008).
[7] Yue Guan and Jennifer Dy. “Sparse probabilistic principal component analysis”. In: Artificial Intelligence and Statistics. PMLR. 2009, pp. 185–192.
[8] Rajiv Khanna et al. “Sparse submodular probabilistic PCA”. In: Artificial Intelli- gence and Statistics. PMLR. 2015, pp. 453–461.
[9] Artin Armagan, Merlise Clyde, and David Dunson. “Generalized beta mixtures of Gaussians”. In: Advances in neural information processing systems 24 (2011).
[10] Prasenjit Ghosh et al. “Asymptotic properties of Bayes risk of a general class of shrinkage priors in multiple hypothesis testing under sparsity”. In: Bayesian Analysis 11.3 (2016), pp. 753–796.
[11] Ray Bai and Malay Ghosh. “High-dimensional multivariate posterior consis- tency under global–local shrinkage priors”. In: Journal of Multivariate Analysis 167 (2018), pp. 157–170.
指導教授 王紹宣(Shao-Hsuan Wang) 審核日期 2022-8-24
推文 facebook   plurk   twitter   funp   google   live   udn   HD   myshare   reddit   netvibes   friend   youpush   delicious   baidu   
網路書籤 Google bookmarks   del.icio.us   hemidemi   myshare   

若有論文相關問題,請聯絡國立中央大學圖書館推廣服務組 TEL:(03)422-7151轉57407,或E-mail聯絡  - 隱私權政策聲明