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Title: | 正規化線性判別分析之穩定性分析 Stability Analysis of Regularized Linear Discriminant Analysis |
Authors: | Chih-Han Shih 施智涵 |
Advisor: | 陳素雲 |
Keyword: | 線性判別分析,非滿秩,主成份分析,特徵值稀疏性,穩定性分析, Linear discriminant analysis,HDLSS,PCA,Eigen-sparsity,Ridge LDA, |
Publication Year : | 2017 |
Degree: | 碩士 |
Abstract: | Fisher線性判別分析常用於處理分類問題,然而在高維度低樣本數的框架下,類別內的樣本共變異矩陣常常是非滿秩矩陣,導致傳統的Fisher線性判別分析無法實行。在過去文獻中有許多方法處理這個難題,像是主成份分析-線性判別分析、零空間-線性判別分析、特徵值稀疏性-線性判別分析、脊-線性判別分析。在這篇論文中,我們針對不同的方法所求出的分類方向的估計進行穩定性分析。 Fisher linear discriminant analysis (LDA) is commonly used in classification problems. However, in high dimension low sample size (HDLSS) scenarios, the within-class sample covariance matrix is often singular, which leads to the failure of LDA. Several discriminant methods were developed in literature to deal with this difficulty, such as PCA-LDA, Null-space LDA, Eigen-sparsity based LDA and Ridge LDA. In this thesis, we analyze the stability for various regularized estimators of discriminant direction derived from different methods. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/69545 |
DOI: | 10.6342/NTU201801133 |
Fulltext Rights: | 有償授權 |
Appears in Collections: | 應用數學科學研究所 |
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