臺灣博碩士論文加值系統

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。

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.

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

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