Abstract
A well-designed graph plays a fundamental role in graph-based semi-supervised learning; however, the topological structure of a constructed neighborhood is unstable in most current approaches, since they are very sensitive to the high dimensional, sparse and noisy data. This generally leads to dramatic performance degradation. To deal with this issue, we developed a relative manifold based semi-supervised dimensionality reduction (RMSSDR) approach by utilizing the relative manifold to construct a better neighborhood graph with fewer short-circuit edges. Based on the relative cognitive law and manifold distance, a relative transformation is used to construct the relative space and the relative manifold. A relative transformation can improve the ability to distinguish between data points and reduce the impact of noise such that it may be more intuitive, and the relative manifold can more truly reflect the manifold structure since data sets commonly exist in a nonlinear structure. Specifically, RMSSDR makes full use of pairwise constraints that can define the edge weights of the neighborhood graph by minimizing the local reconstruction error and can preserve the global and local geometric structures of the data set. The experimental results on face data sets demonstrate that RMSSDR is better than the current state of the art comparing methods in both performance of classification and robustness.
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28 October 2015
Figure 8 of this article shows YaleB and CMU PIE with incorrect legend titles: YaleB (Tr=1900, Te=514, NOC=100) should be YaleB (Tr=1900, Te=514, d=100) (Fig. 8(a)); TIE (Tr=1200, Te=2880, d=100) should be PIE (Tr=1200, Te=2880, d=100) (Fig. 8(b)).
28 October 2015
Figure 8 of this article shows YaleB and CMU PIE with incorrect legend titles: YaleB (Tr=1900, Te=514, NOC=100) should be YaleB (Tr=1900, Te=514, d=100) (Fig. 8(a)); TIE (Tr=1200, Te=2880, d=100) should be PIE (Tr=1200, Te=2880, d=100) (Fig. 8(b)).
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Xianfa Cai is an associate professor of the School of Medical Information Engineering, Guangdong Pharmaceutical University. Cai received his BS and MS degrees from Jiangxi Normal university and SunYat-sen University in 2002 and 2006, respectively, and obtained his PhD degree from South China University of Technology in 2013. His research focuses on machine learning, pattern recognition, and bioinformatics.
Guihua Wen is a professor and doctoral supervisor. In 2005 and 2006, he did visiting research on machine learning and semantic web in School of Electronics and Computer, University of Southampton, UK. His main research interests are computational creativity, machine learning, knowledge discovery and cognitive geometry. Since 2006, he has proposed some original methods based on the computation of cognitive laws that can effectively solve difficult problems in information science. He has been a Council Member of Chinese Association for Artificial Intelligence and a program committee member of many international conferences. He is also a reviewer for China National Natural Science Foundation.
Jia Wei received his BS and MS degrees in computer science from Harbin Institute of Technology in 2003 and 2006, respectively, and his PhD degree in computer science from the South China University of Technology in 2009. He is now a lecturer in the School of Computer Science and Engineering, South China University of Technology. His research fields include machine learning and image retrieval.
Zhiwen Yu is a professor in the School of Computer Science and Engineering, South China University of Technology, Guangzhou, China. Yu is a senior member of IEEE and a senior member of China Computer Federation. He received his BS and MPhil from SunYatsen University in China in 2001 and 2004, respectively, and his PhD degree in computer science from the City University of Hong Kong, China in 2008. His research interests include pattern recognition, bioinformatics, multimedia, intelligent computing, and data mining. Yu has published more than 80 referred journal papers and international conference papers.
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Cai, X., Wen, G., Wei, J. et al. Relative manifold based semi-supervised dimensionality reduction. Front. Comput. Sci. 8, 923–932 (2014). https://doi.org/10.1007/s11704-014-3193-8
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DOI: https://doi.org/10.1007/s11704-014-3193-8