Reversible Discriminant Analysis
Principal component analysis (PCA) and linear discriminant analysis (LDA) have been extended to be a group of classical methods in dimensionality reduction for unsupervised and supervised learning, respectively. However, compared with the PCA, the LDA loses several advantages because of the singular...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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IEEE
2018-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/8534477/ |
| _version_ | 1819170293575319552 |
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| author | Lan Bai Zhen Wang Yuan-Hai Shao Chun-Na Li |
| author_facet | Lan Bai Zhen Wang Yuan-Hai Shao Chun-Na Li |
| author_sort | Lan Bai |
| collection | DOAJ |
| description | Principal component analysis (PCA) and linear discriminant analysis (LDA) have been extended to be a group of classical methods in dimensionality reduction for unsupervised and supervised learning, respectively. However, compared with the PCA, the LDA loses several advantages because of the singularity of its between-class scatter, resulting in singular mapping and restriction of reduced dimension. In this paper, we propose a dimensionality reduction method by defining a full-rank between-class scatter, called reversible discriminant analysis (RDA). Based on the new defined between-class scatter matrix, our RDA obtains a nonsingular mapping. Thus, RDA can reduce the sample space to arbitrary dimension and the mapped sample can be recovered. RDA is also extended to kernel based dimensionality reduction. In addition, PCA and LDA are the special cases of our RDA. Experiments on the benchmark and real problems confirm the effectiveness of the proposed method. |
| first_indexed | 2024-12-22T19:33:06Z |
| format | Article |
| id | doaj.art-2d00a1bc22dc4f0eac24ddc842c25b30 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-22T19:33:06Z |
| publishDate | 2018-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-2d00a1bc22dc4f0eac24ddc842c25b302022-12-21T18:15:03ZengIEEEIEEE Access2169-35362018-01-016725517256210.1109/ACCESS.2018.28812568534477Reversible Discriminant AnalysisLan Bai0Zhen Wang1https://orcid.org/0000-0002-3282-8588Yuan-Hai Shao2Chun-Na Li3https://orcid.org/0000-0001-7033-0089School of Mathematical Sciences, Inner Mongolia University, Hohhot, ChinaSchool of Mathematical Sciences, Inner Mongolia University, Hohhot, ChinaSchool of Economics and Management, Hainan University, Haikou, ChinaZhijiang College, Zhejiang University of Technology, Hangzhou, ChinaPrincipal component analysis (PCA) and linear discriminant analysis (LDA) have been extended to be a group of classical methods in dimensionality reduction for unsupervised and supervised learning, respectively. However, compared with the PCA, the LDA loses several advantages because of the singularity of its between-class scatter, resulting in singular mapping and restriction of reduced dimension. In this paper, we propose a dimensionality reduction method by defining a full-rank between-class scatter, called reversible discriminant analysis (RDA). Based on the new defined between-class scatter matrix, our RDA obtains a nonsingular mapping. Thus, RDA can reduce the sample space to arbitrary dimension and the mapped sample can be recovered. RDA is also extended to kernel based dimensionality reduction. In addition, PCA and LDA are the special cases of our RDA. Experiments on the benchmark and real problems confirm the effectiveness of the proposed method.https://ieeexplore.ieee.org/document/8534477/Between-class scatterdimensionality reductionlinear discriminant analysissupervised learning |
| spellingShingle | Lan Bai Zhen Wang Yuan-Hai Shao Chun-Na Li Reversible Discriminant Analysis IEEE Access Between-class scatter dimensionality reduction linear discriminant analysis supervised learning |
| title | Reversible Discriminant Analysis |
| title_full | Reversible Discriminant Analysis |
| title_fullStr | Reversible Discriminant Analysis |
| title_full_unstemmed | Reversible Discriminant Analysis |
| title_short | Reversible Discriminant Analysis |
| title_sort | reversible discriminant analysis |
| topic | Between-class scatter dimensionality reduction linear discriminant analysis supervised learning |
| url | https://ieeexplore.ieee.org/document/8534477/ |
| work_keys_str_mv | AT lanbai reversiblediscriminantanalysis AT zhenwang reversiblediscriminantanalysis AT yuanhaishao reversiblediscriminantanalysis AT chunnali reversiblediscriminantanalysis |