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Atomic Representation-Based Classification: Theory, Algorithm, and Applications
Wang, Yulong1; Tang, Yuan Yan2; Li, Luoqing3; Chen, Hong4; Pan, Jianjia2
2019-01
Source PublicationIEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
ISSN0162-8828
Volume41Issue:1Pages:6-19
AbstractRepresentation-based classification (RC) methods such as sparse RC (SRC) have attracted great interest in pattern recognition recently. Despite their empirical success, few theoretical results are reported to justify their effectiveness. In this paper, we establish the theoretical guarantees for a general unified framework termed as atomic representation-based classification (ARC), which includes most RC methods as special cases. We introduce a new condition called atomic classification condition (ACC), which reveals important geometric insights for the theory of ARC. We show that under such condition ARC is provably effective in correctly recognizing any new test sample, even corrupted with noise. Our theoretical analysis significantly broadens the range of conditions under which RC methods succeed for classification in the following two aspects: (1) prior theoretical advances of RC are mainly concerned with the single SRC method while our theory can apply to the general unified ARC framework, including SRC and many other RC methods; and (2) previous works are confined to the analysis of noiseless test data while we provide theoretical guarantees for ARC using both noiseless and noisy test data. Numerical results are provided to validate and complement our theoretical analysis of ARC and its important special cases for both noiseless and noisy test data.
KeywordAtomic representation representation-based classification atomic classification condition
DOI10.1109/TPAMI.2017.2780094
URLView the original
Indexed BySCI
Language英语
WOS Research AreaComputer Science ; Engineering
WOS SubjectComputer Science, Artificial Intelligence ; Engineering, Electrical & Electronic
WOS IDWOS:000452434800002
PublisherIEEE COMPUTER SOC
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Cited Times [WOS]:2   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionUniversity of Macau
Affiliation1.Chengdu Univ, Sch Informat Sci & Engn, Chengdu 610106, Sichuan, Peoples R China;
2.Univ Macau, Fac Sci & Technol, Macau 999078, Peoples R China;
3.Hubei Univ, Fac Math & Stat, Wuhan 430062, Hubei, Peoples R China;
4.Univ Texas Arlington, Dept Comp Sci & Engn, Arlington, TX 76019 USA
Recommended Citation
GB/T 7714
Wang, Yulong,Tang, Yuan Yan,Li, Luoqing,et al. Atomic Representation-Based Classification: Theory, Algorithm, and Applications[J]. IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE,2019,41(1):6-19.
APA Wang, Yulong,Tang, Yuan Yan,Li, Luoqing,Chen, Hong,&Pan, Jianjia.(2019).Atomic Representation-Based Classification: Theory, Algorithm, and Applications.IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE,41(1),6-19.
MLA Wang, Yulong,et al."Atomic Representation-Based Classification: Theory, Algorithm, and Applications".IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 41.1(2019):6-19.
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