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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳定立(Ting-Li Chen) | |
| dc.contributor.author | Wen-Shao He | en |
| dc.contributor.author | 何文劭 | zh_TW |
| dc.date.accessioned | 2021-06-17T00:43:13Z | - |
| dc.date.available | 2021-02-10 | |
| dc.date.copyright | 2020-02-10 | |
| dc.date.issued | 2020 | |
| dc.date.submitted | 2020-02-05 | |
| dc.identifier.citation | [CR92] CY Chork and Peter J Rousseeuw. Integrating a high-breakdown option into discriminant analysis in exploration geochemistry. Journal of
Geochemical Exploration, 43(3):191–203, 1992. [DKK+19] Ilias Diakonikolas, Gautam Kamath, Daniel Kane, Jerry Li, Ankur Moitra, and Alistair Stewart. Robust estimators in high-dimensions without the computational intractability. SIAM Journal on Computing, 48(2):742–864, 2019. [Don82] David L Donoho. Breakdown properties of multivariate location estimators. Technical report, Technical report, Harvard University, Boston. URL http://www-stat. stanford …, 1982. [FE08] Hironori Fujisawa and Shinto Eguchi. Robust parameter estimation with a small bias against heavy contamination. J. Multivar. Anal., 99(9):2053–2081, October 2008. [FT74] Jerome H Friedman and John W Tukey. A projection pursuit algorithm for exploratory data analysis. IEEE Transactions on computers, 100(9):881–890, 1974. [Ham68] Frank R Hampel. Contribution to the theory of robust estimation. Ph. D. Thesis, University of California, Berkeley, 1968. [Ham74] Frank R. Hampel. The influence curve and its role in robust estimation. Journal of the American Statistical Association, 69(346):383–393, 1974. HD04] Mia Hubert and Katrien Driessen. Fast and robust discriminant analysis. Computational Statistics Data Analysis, 45:301–320, 03 2004. [HF00] Xuming He and Wing Fung. High breakdown estimation for multiple populations with applications to discriminant analysis. Journal of Multivariate Analysis, 72:151–162, 02 2000. [HM97] Douglas M. Hawkins and Geoffrey J. McLachlan. High-breakdown linear discriminant analysis. Journal of the American Statistical Association, 92(437):136–143, 3 1997. [HR09] Peter J Huber and Elvezio M Ronchetti. Robust statistics; 2nd ed. Wiley Series in Probability and Statistics. Wiley, Hoboken, NJ, 2009. [HRRS11] F.R. Hampel, E.M. Ronchetti, P.J. Rousseeuw, and W.A. Stahel. Robust Statistics: The Approach Based on Influence Functions. Wiley Series in Probability and Statistics. Wiley, 2011. [Hub64] Peter J. Huber. Robust estimation of a location parameter. Ann. Math. Statist., 35(1):73–101, 03 1964. [Hub85] Peter J. Huber. Projection pursuit. Ann. Statist., 13(2):435–475, 06 1985. [LRV16] Kevin A Lai, Anup B Rao, and Santosh Vempala. Agnostic estimation of mean and covariance. In 2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS), pages 665–674. IEEE, 2016. [Mar76] Ricardo Antonio Maronna. Robust m-estimators of multivariate location and scatter. Ann. Statist., 4(1):51–67, 01 1976. [MB98] A.M. Martinez and R. Benavente. The ar face database. Technical Report 24, Computer Vision Center, 06 1998. [PB10] Ana M Pires and Jo˜ao A Branco. Projection-pursuit approach to robust linear discriminant analysis. Journal of Multivariate Analysis, 101(10):2464–2485, 2010. [Rou81] Peter J Rousseeuw. A new infinitesimal approach to robust estimation. Zeitschrift f¨ur Wahrscheinlichkeitstheorie und verwandte Gebiete, 56(1):127–132, 1981. [Rou85] Peter Rousseeuw. Multivariate estimation with high breakdown point. Mathematical Statistics and Applications Vol. B, pages 283–297, 01 1985. [Sta81] Fachgruppe Fuer Statistik. Breakdown of covariance estimators. Research Report, 1981. [Ste79] G.W. Stewart. Pertubation bounds for the definite generalized eigenvalue problem. Linear algebra and its applications, 23:69–85, 1979. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/66560 | - |
| dc.description.abstract | 線性判別分析可最大程度地提高組間差異與組內差異的比率，它被廣泛用於監督維度縮減中。在傳統的線性判別分析中，判別空間會被標籤錯誤的數據嚴重影響。為了克服這個問題，我們提出了基於伽馬散度的穩健線性判別分析。本文將介紹伽馬線性判別分析算法，並透過影響函數分析其穩健性。我們也藉由模擬資料與人臉辨識資料來展現新方法的優越性。 | zh_TW |
| dc.description.abstract | Linear discriminant analysis (LDA) which maximizes the ratio of the between-class variance to the within-class variance is widely used in supervised dimension reduction. In the traditional LDA, the discriminant space can be badly affected by the mislabeled data. To overcome this issue, we propose a robust linear discriminant analysis based on the γ-divergence which is a more robust measure than the Kullback-Leibler divergence. In this thesis, we will introduce the γ-LDA algorithm and analyze its robustness by the influence function. Furthermore, we will show the superior performance of γ-LDA on the simulated examples as well as face image data. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-17T00:43:13Z (GMT). No. of bitstreams: 1 ntu-109-R07246009-1.pdf: 3115195 bytes, checksum: 6153c7978f698b6983e48f1feee29fdd (MD5) Previous issue date: 2020 | en |
| dc.description.tableofcontents | Acknowledgements i
Abstract ii 1 Introduction 1 1.1 Linear Discriminant Analysis . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Robust Linear Discriminant Analysis . . . . . . . . . . . . . . . . . . 3 2 Robustness of Linear Discriminant Analysis 4 2.1 Robust Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.1.1 Measurement of Robustness . . . . . . . . . . . . . . . . . . . 5 2.1.2 M-estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Robustness of Linear Discriminant Analysis . . . . . . . . . . . . . . 8 3 The Minimum γ-Divergence Estimation 12 4 γ-LDA Algorithm 16 4.1 Model Specification and Estimation . . . . . . . . . . . . . . . . . . . 17 4.2 Plug-in γ-LDA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.3 Projection Pursuit γ-LDA . . . . . . . . . . . . . . . . . . . . . . . . 20 4.3.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 4.3.2 Projection Pursuit . . . . . . . . . . . . . . . . . . . . . . . . 21 4.4 Simulation and Compression of γ-LDA . . . . . . . . . . . . . . . . . 23 5 Robustness of γ-LDA 29 6 Real Data 32 7 Discussion and Future Work 34 | |
| dc.language.iso | en | |
| dc.subject | 穩健統計學 | zh_TW |
| dc.subject | 線性判別分析 | zh_TW |
| dc.subject | 降維 | zh_TW |
| dc.subject | γ-散度 | zh_TW |
| dc.subject | 影響函數 | zh_TW |
| dc.subject | Robust statistics | en |
| dc.subject | Linear discriminant analysis | en |
| dc.subject | Dimension reduction | en |
| dc.subject | γ-divergence | en |
| dc.subject | Influence function | en |
| dc.title | 使用伽馬散度之穩健線性判別分析法 | zh_TW |
| dc.title | Robust linear discriminant analysis based on γ-divergence | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 108-1 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 陳素雲(Su-Yun Huang),杜憶萍(I-Ping Tu),王偉仲(Wei-Chung Wang) | |
| dc.subject.keyword | 穩健統計學,線性判別分析,降維,γ-散度,影響函數, | zh_TW |
| dc.subject.keyword | Robust statistics,Linear discriminant analysis,Dimension reduction,γ-divergence,Influence function, | en |
| dc.relation.page | 38 | |
| dc.identifier.doi | 10.6342/NTU201901737 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2020-02-06 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 應用數學科學研究所 | zh_TW |
| 顯示於系所單位： | 應用數學科學研究所 | |
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