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Ratio sum formula for dimensionality reduction

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Abstract

High-dimensional data analysis often suffers the so-called curse of dimensionality. Therefore, dimensionality reduction is usually carried out on the high-dimensional data before the actual analysis, which is a common and efficient way to eliminate this effect. And the popular trace ratio criterion is an extension of the original linear discriminant analysis (LDA) problem, which involves a search of a transformation matrix W to embed high-dimensional space into a low-dimensional space to achieve dimensionality reduction. However, the trace ratio criterion tends to obtain projection direction with very small variance, which the subset after the projection is diffcult to present the most representative information of the data with maximum efficiency. In this paper, we target on this problem and propose the ratio sum formula for dimensionality reduction. Firstly, we analyze the impact of this trend. Then in order to solve this problem, we propose a new ratio sum formula as well as the solution. In the end, we perform experiments on the Yale-B, ORL, and COIL-20 data sets. The theoretical studies and actual numerical analysis confirm the effectiveness of the proposed method.

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Acknowledgments

The authors would like to thank the editors and anonymous reviews for providing useful suggestion to improve the quality of the paper. This work was partially supported by National R&D Program of China 2018YFB1802100, Department of Science and Technology at Guangdong Province with Grant no. 2018B030338001, 2018B010107003, 2018B010115002 and 2015B010127015, and National Nature Science Foundation of China(No. 61974035).

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Authors and Affiliations

  1. School of Information Engineering, Guangdong University of Technology, Guangzhou, Guangdong, 510006, China

    Ke Liang, XiaoJun Yang & YuXiong Xu

  2. Synergy Innovation Institute of GDUT, Heyuan, Guangdong, 517000, China

    XiaoJun Yang

  3. School of Computer Science and the Center for Optical Imagery Analysis and Learning, Northwestern Polytechnical University, Xi’an, 710072, China

    Rong Wang & Feiping Nie

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  1. Ke Liang
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  5. Feiping Nie
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Correspondence to XiaoJun Yang.

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Liang, K., Yang, X., Xu, Y. et al. Ratio sum formula for dimensionality reduction. Multimed Tools Appl 80, 4367–4382 (2021). https://doi.org/10.1007/s11042-020-09782-w

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  • DOI: https://doi.org/10.1007/s11042-020-09782-w

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