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Relative manifold based semi-supervised dimensionality reduction

Frontiers of Computer Science 2014年第6期8卷 923-932页

作者： Xianfa CAI Guihua WEN Jia WEI Zhiwen YU School of Medical Information Engineering Guangdong Pharmaceutical University Guangzhou 510006 China School of Computer Science and Engineering South China University of Technology Guangzhou 510006 China Shenzhen Key Laboratory of High Performance Data Mining Shenzhen 518055 China

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 semisupervised 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.

关键词： cognitive law relative transformation relative manifold local reconstruction semi-supervised learning

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