正規化線性判別分析之穩定性分析

Stability Analysis of Regularized Linear Discriminant Analysis

施智涵(Chih-Han Shih)

指導教授 ： 陳素雲

共同指導教授 ： 陳宏

國立臺灣大學/理學院/應用數學科學研究所/碩士(2017年)

https://doi.org/10.6342/NTU201801133

摘要

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。

關鍵字

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

並列摘要

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.

並列關鍵字

Linear discriminant analysis ； HDLSS ； PCA ； Eigen-sparsity ； Ridge LDA

參考文獻

[1] P. N. Belhumeur, J. P. Hespanha, and D. J. Kriegman. Eigenfaces vs. fisherfaces: Recognition using class specific linear projection. IEEE Transactions on Pattern Analysis and Machine Intelligence, 19(7):711–720, 1997.

[2] L.-F. Chen, H.-Y. M. Liao, M.-T. Ko, J.-C. Lin, and G.-J. Yu. A new lda-based face recognition system which can solve the small sample size problem. Pattern Recogni- tion, 33(10):1713–1726, 2000.

[3] K. Fukunaga. Introduction to Statistical Pattern Recognition. Academic press, 2013.

[4] L. Li, R. D. Cook, and C.-L. Tsai. Partial inverse regression. Biometrika, pages 615–625, 2007.

[5] J. Ye and T. Xiong. Computational and theoretical analysis of null space and orthogo- nal linear discriminant analysis. Journal of Machine Learning Research, 7(Jul):1183– 1204, 2006.