高維度環境下Kronecker包絡主成分分析的漸近性

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：81

、訪客IP：18.188.119.67

姓名

林祥曆(Siang-Li Lin) 查詢紙本館藏

畢業系所

統計研究所

論文名稱

高維度環境下Kronecker包絡主成分分析的漸近性
(On the asymptotics of the Kronecker envelope principal component analysis in high-dimensional settings)

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
★ gamma-SUP on PCA

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]

至系統瀏覽論文 (2026-8-1以後開放)

摘要(中)

主成分分析（PCA）是一種廣泛運用於資料預處理步驟中的降維方法，但在低信噪比的高維資料分析中，PCA的性能可能受到限制。為了解決這個問題，先前的研究提出了Kronecker包絡主成分分析（KEPCA）可作為PCA的替代方法。在本文中，我們介紹了Wang et al.(2024)在高維度理論中提出的KEPCA的一致性和漸近常態性，同時，我們經由模擬實驗和實際資料分析將其與經典PCA進行比較，逕而驗證了理論結果。

摘要(英)

Principal Component Analysis (PCA) is a widely used dimension reduction method in data preprocessing, but its performance may be limited in the analysis of high-dimensional data with low signal-to-noise ratios. To address this issue, previous research proposed Kronecker Envelope Principal Component Analysis (KEPCA) as an alternative to PCA. In this article, we introduce the consistency and asymptotic normality of KEPCA, which is proposed by Wang et al.(2024) and we compare it with classical PCA through simulation experiments and real data analysis.

關鍵字(中)

★ 漸近常態性
★ 維度縮減
★ 高維度小樣本
★ Kronecker包絡
★ 主成分分析

關鍵字(英)

論文目次

一緒論 1
二文獻回顧 3
2.1 Kronecker包絡主成分分析 3
2.1.1 KEPCA模型 3
2.1.2 固定維數下的漸近常態性 5
2.2 PCA和KEPCA間的漸近效率比較 5
2.3 高維度下的KEPCA 6
2.3.1 統計模型 6
2.3.2 參數估計式 7
2.3.3 蓋理論應用在MPCA的尖峰共變異模型 8
2.4 MPCA的漸近性 12
2.5 KEPCA的漸近性 15
三數值分析 17
3.1 KEPCA模型 17
四實際資料分析 25
4.1 Olivetti 人臉資料 25
4.2 胸部超音波圖像資料 29
4.3 擴散核磁造影 32
五結論 36
參考文獻 37

參考文獻

Al-Dhabyani, W., Gomaa, M., Khaled, H., and Fahmy, A. (2020). Dataset of breast ultrasound images. Data in brief, 28:104863.
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). γ-SUP: A clustering algorithm for cryo-electron microscopy images of asymmetric particles. Annals of Applied Statistics, 8:259–285.
Chung, S.-C., Lin, H.-H., Niu, P.-Y., Huang, S.-H., Tu, I.-P., and Chang, W.-H. (2020a). Pre-pro is a fast pre-processor for single-particle cryo-EM by enhancing 2D classification. Communications Biology, 3:1–12.
Chung, S.-C., Wang, S.-H., Niu, P.-Y., Huang, S.-Y., Chang, W.-H., and Tu, I.-P. (2020b). Two-stage dimension reduction for noisy high-dimensional images and application to
cryogenic electron microscopy. Annals of Mathematical Sciences and Applications, 5:283–316.
Huang, S.-H. and Huang, S.-Y. (2021). On the asymptotic normality and eﬀiciency of
Kronecker envelope principal component analysis. Journal of Multivariate Analysis, accepted.
Hung, H., Wu, P.-S., Tu, I.-P., and Huang, S.-Y. (2012). On multilinear principal component analysis of order-two tensors. Biometrika, 99:569–583.
Johnstone, I. M. (2001). On the distribution of the largest eigenvalue in principal components analysis. Annals of Statistics, 29:295–327.
Konishi, S. and Kitagawa, G. (1996). Generalised information criteria in model selection. Biometrika, 83(4):875–890.
Li, B., Kim, K. M., and Altman, N. (2010). On dimension folding of matrix or array-valued statistical objects. Annals of Statistics, 38:1094–1121.
Marshall, A. W., Olkin, I., and Arnold, B. (2011). Inequalities: Theory of Majorization and Its Applications. Springer, New York, second edition.
Paul, D. (2007). Asymptotics of sample eigenstructure for a large dimensional spiked covariance model. Statistica Sinica, 17:1617–1642.
Schott, J. R. (2014). Tests for Kronecker envelope models in multilinear principal components analysis. Biometrika, 101:978–984.
Tu, I. P., Huang, S. Y., and Hsieh, D. N. (2019). The generalized degrees of freedom of multilinear principal component analysis. Journal of Multivariate Analysis, 173:26–37.
Wang, S.-H., Huang, S.-H., and Huang, S.-Y. (2024). On asymptotic normality of mpca in high dimension. unpublished manuscript.
Yata, K. and Aoshima, M. (2009). PCA consistency for non-Gaussian data in high dimension, low sample size context. Communications in Statistics—Theory and Methods, 38:2634–2652.
Yata, K. and Aoshima, M. (2013). PCA consistency for the power spiked model in high-dimensional settings. Journal of Multivariate Analysis, 122:334–354.
Ye, J. (2004). Generalized low rank approximations of matrices. In Proceedings of the twenty-first international conference on Machine learning, page 112.

指導教授

王紹宣

審核日期

2024-7-10

推文