gamma-SUP on PCA

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姓名

蔡姵綾(Pei-Ling Tsai) 查詢紙本館藏

畢業系所

統計研究所

論文名稱

(gamma-SUP on PCA)

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
★ Bayesian method for sparse principal component analysis	★ 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
★ 隱私差分應用於聯邦式水平分割主成分分析	★ Contrastive Principal Component Analysis for High-Dimension, Low-Sample-Size Data with Noise-Reduction
★ γ-SUP 演算法在 NBA 資料分析上的應用	★ 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
★ 高維度環境下Kronecker包絡主成分分析的漸近性

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至系統瀏覽論文 (2026-8-1以後開放)

摘要(中)

主成分分析（PCA）是一種廣泛使用的統計工具，用於降低大型資料集的維度，同時保留大部分資訊。一個關鍵是將 PCA 應用於聚類分析，這在異常檢測、生物學和醫學等領域至關重要。傳統的基於模型的方法對模型錯誤指定很敏感，並且需要預先定義聚類的數量，可能會導致偏差的結果或不穩定的推理。在本文中，我們提出了一種新穎的 PCA 方法，稱為 γ-SUP PCA，它將 γ-SUP 方法與 PCA 結合，用來避免了指定聚類數量和特定的模型選擇，同時有效地提取重要特徵。數值研究將證明所提出方法的穩健性能。

摘要(英)

Principal component analysis (PCA) is a widely used statistical tool for reducing the dimensionality of large data sets while retaining most of the information. A key area of interest is applying PCA to cluster analysis, which is crucial in fields such as anomaly detection, biology, and medicine. Traditional model-based approaches are sensitive to model mis-specification and require a predefined number of clusters, potentially leading to biased results or unstable inferences. In this article, we propose a novel PCA method, γ-SUP PCA, which combines the γ-SUP approach with PCA. This method circumvents the need to specify the number of clusters and model selection, while effectively extracting important features. Numerical studies will demonstrate the robust performance of the proposed method.

關鍵字(中)

★ 聚類演算法
★ γ-散度
★ γ-自我更新過程
★ 主成分分析
★ 自我更新過程

關鍵字(英)

★ clustering algorithm
★ γ-divergence
★ γ-SUP
★ principal component analysis
★ self-updating process

論文目次

1 Introduction 1
2 Review of γ-self update process 3
2.1 γ-divergence 3
2.2 The q-Gaussian distribution 3
2.3 γ-SUP 6
3 Method 9
3.1 Mixture probabilistic PCA model 9
3.2 γ-SUP PCA 9
3.3 Rank selection of feature matrix B 15
4 Numerical Study 16
4.1 Scenario 1: two clusters 16
4.2 Scenario 2 three clusters 19
5 Data analysis 22
5.1 NBA Dataset 22
5.2 Diabetes Dataset 27
6 Conclusion 32
References 33

參考文獻

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2.Chen, T.-L., Hsieh, D.-N., Hung, H., Tu, I.-P., Wu, P.-S., Wu, Y.-M., Chang, W.-H., and Huang, S.-Y. (2014). gamma-sup: A clustering algorithm for cryo-electron microscopy images of asymmetric particles. Annals of Applied Statistics,8(1):259–285.
3.Chen, T.-L. and Shiu, S.-Y. (2007). A new clustering algorithm based on self-updating process. JSM proceedings, statistical computing section, Salt Lake City, Utah, pages
2034–2038.
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6.Fujisawa, H. and Eguchi, S. (2008). Robust parameter estimation with a small bias against heavy contamination. Journal of Multivariate Analysis, 99(9):2053–2081.
7.Maćkiewicz, A. and Ratajczak, W. (1993). Principal components analysis (pca). Computers & Geosciences, 19(3):303–342.
8.Morissette, L. and Chartier, S. (2013). The k-means clustering technique: General considerations and implementation in mathematica. Tutorials in Quantitative Methods for Psychology, 9(1):15–24.
9.Nakagawa, T. and Hashimoto, S. (2020). Robust bayesian inference via γ-divergence.Communications in Statistics-Theory and Methods, 49(2):343–360.

指導教授

王紹宣(Shao-Hsuan Wang)

審核日期

2024-7-10

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