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Simultaneous variable selection and class fusion with penalized distance criterion based classifiers
Sheng, Ying1; Wang, Qihua1,2
2019-05-01
Source PublicationCOMPUTATIONAL STATISTICS & DATA ANALYSIS
ISSN0167-9473
Volume133Pages:138-152
AbstractTwo new methods are proposed to solve the problem of constructing multiclass classifiers, selecting important variables for classification and determining corresponding discriminative variables for each pair of classes simultaneously in the high-dimensional setting. Different from existing methods, which are based on the separate estimation of the precision matrix and mean vectors, the proposed methods construct classifiers by estimating products of the precision matrix and mean vectors or all discriminant directions directly with appropriate penalties. This leads to the use of the distance criterion instead of the log-likelihood used in the existing literature. The proposed methods can not only consistently select important variables for classification but also consistently determine corresponding discriminative variables for each pair of classes. For the multiclass classification problem, conditional misclassification error rates of classifiers constructed by the proposed methods converge to the misclassification error rate of the Bayes rule in probability and rates of convergence are also obtained. Finally, simulations and the real data analysis well demonstrate good performances of the proposed methods in comparison with existing methods. (C) 2018 Elsevier B.V. All rights reserved.
KeywordLinear discriminant analysis Discriminant directions Variable selection Class fusion Misclassification error rate
DOI10.1016/j.csda.2018.09.002
Language英语
Funding ProjectNational Natural Science Foundation of China[11871460] ; National Natural Science Foundation of China[11331011] ; program for Creative Research Group in China[61621003] ; Key Lab of Random Complex Structure and Data Science, CAS, China
WOS Research AreaComputer Science ; Mathematics
WOS SubjectComputer Science, Interdisciplinary Applications ; Statistics & Probability
WOS IDWOS:000460719200010
PublisherELSEVIER SCIENCE BV
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/33337
Collection应用数学研究所
Corresponding AuthorWang, Qihua
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
2.Zhejiang Gongshang Univ, Sch Stat & Math, Hangzhou 310018, Zhejiang, Peoples R China
Recommended Citation
GB/T 7714
Sheng, Ying,Wang, Qihua. Simultaneous variable selection and class fusion with penalized distance criterion based classifiers[J]. COMPUTATIONAL STATISTICS & DATA ANALYSIS,2019,133:138-152.
APA Sheng, Ying,&Wang, Qihua.(2019).Simultaneous variable selection and class fusion with penalized distance criterion based classifiers.COMPUTATIONAL STATISTICS & DATA ANALYSIS,133,138-152.
MLA Sheng, Ying,et al."Simultaneous variable selection and class fusion with penalized distance criterion based classifiers".COMPUTATIONAL STATISTICS & DATA ANALYSIS 133(2019):138-152.
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