正規化線性判別分析之穩定性分析

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.