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A multiple attributes convolution kernel with reproducing property

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Abstract

Various kernel-based methods have been developed with great success in many fields, but very little research has been published that is concerned with a multiple attribute kernel in reproducing kernel Hilbert space (RKHS). In this paper, we propose a novel elastic kernel called a multiple attribute convolution kernel with reproducing property (MACKRP) and present improved classification results over conventional approaches in the RKHS rather than the more commonly used Hilbert space. The MACKRP consists of two major steps. First, we find the basic solution of a generalized differential operator by the delta function, and then we design a convolution function using this solution. This convolution function is proven to be a specific reproducing kernel called a convolution reproducing kernel (CRK) in H 3-space. Second, we prove that the CRK satisfies the condition of Mercer kernel. And the CRK is composed of three attributes (L 1-norm, L 2-norm and Laplace kernel), and each attribute can capture a different feature, with all attributes generating a novel kernel which we call an MACKRP. The experimental results demonstrate that the MACKRP possesses approximation and regularization performance and that classification results are consistently comparable or superior to a number of other state-of-the-art kernel functions.

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Acknowledgments

This work was supported by National High Technology Research and Development Program (863 Program) of China under Grant (2014AA015104), MOE Youth Project of Humanities and Social Sciences (15YJC860034), National Nature Science Foundation of China (61472002, 61005010), Anhui Provincial Natural Science Foundation (1408085QF108), Key Construction Disciplines of Hefei University (2014XK08), Anhui Provincial Natural Science Foundation (1308085MF84), Support Project for Excellent Young Talent in College of Anhui Province (X.F.Wang), Hefei University Scientific Research Fund (12KY04ZD, 14RC12), Sino$-$UK Higher Education Research Partnership for PhD Studies (CSC, NO. 201301310003) (Andrew Abel, PhD, University of Stirling, Scotland).

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Authors and Affiliations

  1. School of Computer Science and Technology, Anhui University, Hefei, 230601, Anhui, People’s Republic of China

    Lixiang Xu, Cheng Zhang & Bin Luo

  2. Department of Mathematics and Physics, Hefei University, Hefei, 230601, Anhui, People’s Republic of China

    Lixiang Xu, Xiu Chen & Xin Niu

  3. Hefei VRview Information Technology Co., Ltd, Hefei, 230088, Anhui, People’s Republic of China

    Lixiang Xu

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  1. Lixiang Xu
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  2. Xiu Chen
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  3. Xin Niu
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  4. Cheng Zhang
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  5. Bin Luo
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Correspondence to Bin Luo.

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Xu, L., Chen, X., Niu, X. et al. A multiple attributes convolution kernel with reproducing property. Pattern Anal Applic 20, 485–494 (2017). https://doi.org/10.1007/s10044-015-0514-y

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