Robust Q-mode principal component analysis in L1

被引：20

作者：

Choulakian, V ^{[1
]}

机构：

[1] Univ Moncton, Fac Sci, Dept Math & Stat, Moncton, NB E1A 3E9, Canada

来源：

COMPUTATIONAL STATISTICS & DATA ANALYSIS | 2001年 / 37卷 / 02期

基金：

加拿大自然科学与工程研究理事会;

关键词：

principal components; L-1-norm; Q-analysis; R-analysis; outliers; A-estimator of scale; extended simple structure; projection pursuit;

D O I：

10.1016/S0167-9473(01)00005-6

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

We propose principal component analysis (PCA) of a data set based on the L-1-norm. We distinguish between Q-mode and R-mode analyses. The Q-mode L-1 principal components are sequentially calculated by an enumeration procedure. We show that the Q-mode L-1-norm PCA is a constrained version of R-mode L-2-norm. PCA. Two generalizations are proposed, robustification and extension of Thurston's simple structure. Robustification is achieved by replacing the L-2-norm. by an efficient robust A-estimator of scale based on Tukey's biweight function. Extended simple structure is used to discard redundant variables. Examples are provided. (C) 2001 Elsevier Science B.V. All rights reserved.

引用

页码：135 / 150

页数：16

共 50 条

[1] A fast algorithm for the computation of robust Q-mode principal component analysis in L1
Almhana, J
Choulakian, V
[J]. 16TH ANNUAL INTERNATIONAL SYMPOSIUM ON HIGH PERFORMANCE COMPUTING SYSTEMS AND APPLICATIONS, PROCEEDINGS, 2002, : 127 - 132
[2] Reweighted l1 Algorithm for Robust Principal Component Analysis
Hoai Minh Le
Vo Xuanthanh
[J]. ADVANCED COMPUTATIONAL METHODS FOR KNOWLEDGE ENGINEERING (ICCSAMA 2019), 2020, 1121 : 133 - 142
[3] Q-mode versus R-mode Principal Component Analysis for Linear Discriminant Analysis (LDA)
Lee, Loong Chuen
Liong, Choong-Yeun
Jemain, Abdul Aziz
[J]. 3RD ISM INTERNATIONAL STATISTICAL CONFERENCE 2016 (ISM III): BRINGING PROFESSIONALISM AND PRESTIGE IN STATISTICS, 2017, 1842
[4] On principal component analysis in L1
Li, BB
Martin, EB
Morris, AJ
[J]. COMPUTATIONAL STATISTICS & DATA ANALYSIS, 2002, 40 (03) : 471 - 474
[5] Robust multivariate L1 principal component analysis and dimensionality reduction
Gao, Junbin
Kwan, Paul W.
Guo, Yi
[J]. NEUROCOMPUTING, 2009, 72 (4-6) : 1242 - 1249
[6] Robust L1 principal component analysis and its Bayesian variational inference
Gao, Junbin
[J]. NEURAL COMPUTATION, 2008, 20 (02) : 555 - 572
[7] Mixture robust L1 probabilistic principal component regression and soft sensor application
Zhu, Pengbo
Yang, Xianqiang
Zhang, Hang
[J]. CANADIAN JOURNAL OF CHEMICAL ENGINEERING, 2020, 98 (08): : 1741 - 1756
[8] Transposition invariant principal component analysis in L1 for long tailed data
Choulakian, V
[J]. STATISTICS & PROBABILITY LETTERS, 2005, 71 (01) : 23 - 31
[9] Robust Principal Component Analysis Based On L1-2 Metric
Zhang, Fanlong
Yang, Zhangjing
Wan, Minghua
Yang, Guowei
[J]. PROCEEDINGS 2017 4TH IAPR ASIAN CONFERENCE ON PATTERN RECOGNITION (ACPR), 2017, : 394 - 398
[10] USE OF Q-MODE FACTOR-ANALYSIS FOR REGIONALIZATION
TOPCHIYEV, AG
[J]. SOVIET GEOGRAPHY REVIEW AND TRANSLATION, 1976, 17 (02): : 94 - 100

← 1 2 3 4 5 →