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Robust sparsity-preserved learning with application to image visualization

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Abstract

Linear subspace learning is of great importance for the purpose of visualization of high-dimensional observations. Sparsity-preserved learning (SPL) is a recently developed technique for linear subspace learning. Its objective function is formulated by using the \(\ell _2\)-norm, which implies that the obtained projection vectors are likely to be distorted by outliers. In this paper, we develop a new SPL algorithm called SPL-L1 based on the \(\ell _1\)-norm instead of the \(\ell _2\)-norm. The proposed approach seeks projection vectors by minimizing a reconstruction error subject to a constraint of samples dispersion, both of which are defined using the \(\ell _1\)-norm. As a robust alternative, SPL-L1 works well in the presence of atypical samples. We design an iterative algorithm under the framework of bound optimization to solve the projection vectors of SPL-L1. The experiments on image visualization demonstrate the superiority of the proposed method.

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Notes

  1. The \(\ell _1\)-norm has been used once in the construction of the \(\ell _1\)-graph.

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Acknowledgments

The authors would like to thank the anonymous referees for the constructive comments, which are helpful to improve the paper.

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Authors and Affiliations

  1. Key Laboratory of Child Development and Learning Science of Ministry of Education, Research Center for Learning Science, Southeast University, Nanjing, 210096, Jiangsu, China

    Haixian Wang & Wenming Zheng

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  1. Haixian Wang
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  2. Wenming Zheng
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Correspondence to Haixian Wang.

Additional information

This work was supported in part by the National Basic Research Program of China under grant 2011CB302202, in part by the National Natural Science Foundation of China under Grant 61075009, in part by the Natural Science Foundation of Jiangsu Province under Grant BK2011595, in part by the Program for New Century Excellent Talents in University of China, and in part by the Qing Lan Project of Jiangsu Province.

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Wang, H., Zheng, W. Robust sparsity-preserved learning with application to image visualization. Knowl Inf Syst 39, 287–304 (2014). https://doi.org/10.1007/s10115-012-0605-7

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