Locality preserving projection based on Euler representation |
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| Affiliation: | 1. Faculty of Information Technology, Beijing University of Technology, Beijing 100124, China;2. Discipline of Business Analytics, The University of Sydney Business School, The University of Sydney, NSW 2006, Australia;3. Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116024, China;1. Department of Electronic Engineering, National Taipei University of Technology, Taipei City 10608, Taiwan;2. Department of Communication Engineering, National Central University, Taoyuan City 320, Taiwan;1. Department of Business Administration, Wonkwang University, 460 Iksandae-ro, Iksan, Jeonbuk, South Korea;2. Engineering Research Center on Cloud Computing & Internet of Things and E-commerce Intelligence of Fujian Universities Quanzhou Normal University, No. 398, Donghai Street, Fengze District, Quanzhou 362000, China;3. School of Economics and Management, Xinyu University, No. 2666, Yangguang Street, Xinyu 338004, China;1. Yango University, Fuzhou 350015, China;2. Department of Public Finance and Taxation, National Kaohsiung University of Science and Technology , Kaohsiung City, 80778, Taiwan;3. Department of International Business, National Kaohsiung University of Science and Technology, Kaohsiung City 80778, Taiwan;1. Haian Senior School of Jiangsu Province, Nantong 226600, China;2. College of Physical Education, China University of Mining and Technology, Xuzhou 221000, China |
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| Abstract: | Locality preserving projection (LPP) is a widely used linear dimensionality reduction method, which preserves the locality structure of the original data. Motivated by the fact that kernel technique can capture nonlinear similarity of features and help to improve separability between nearby data points, this paper proposes locality preserving projection model based on Euler representation (named as ELPP). This model first projects the data into a complex space with Euler representation, then learns the dimensionality reduction projection with preserving locality structure in this complex space. We also extend ELPP to F-ELPP by replacing the squared F-norm with F-norm, which will weaken the exaggerated errors and be more robustness to outliers. The optimization algorithms of the two models are given, and the convergence of F-ELPP is proved. A large number of experiments on several public databases have demonstrated that the two proposed models have good robustness and feature extraction ability. |
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| Keywords: | Locality preserving projection Euler representation Dimensionality reduction |
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