An optimization criterion for generalized marginal Fisher analysis on undersampled problems |
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Authors: | Wu-Yi Yang Sheng-Xing Liu Tai-Song Jin Xiao-Mei Xu |
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Affiliation: | [1]Key Laboratory of Underwater Acoustic Communication and Marine Information Technology of the Ministry of Education, Xiamen University, Xiamen 361005, PRC [2]College of Oceanography and Environmental Science, Xiamen University, Xiamen 361005, PRC [3]School of Information Science and Technology, Xiamen University, Xiamen 361005, PRC |
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Abstract: | Marginal Fisher analysis (MFA) not only aims to maintain the original relations of neighboring data points of the same class
but also wants to keep away neighboring data points of the different classes. MFA can effectively overcome the limitation
of linear discriminant analysis (LDA) due to data distribution assumption and available projection directions. However, MFA
confronts the undersampled problems. Generalized marginal Fisher analysis (GMFA) based on a new optimization criterion is
presented, which is applicable to the undersampled problems. The solutions to the proposed criterion for GMFA are derived,
which can be characterized in a closed form. Among the solutions, two specific algorithms, namely, normal MFA (NMFA) and orthogonal
MFA (OMFA), are studied, and the methods to implement NMFA and OMFA are proposed. A comparative study on the undersampled
problem of face recognition is conducted to evaluate NMFA and OMFA in terms of classification accuracy, which demonstrates
the effectiveness of the proposed algorithms. |
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Keywords: | Linear discriminant analysis (LDA) dimension reduction marginal Fisher analysis (MFA) normal MFA (NMFA) orthogonal MFA (OMFA) |
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