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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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References

  1. Lu H et al (2011) On feature combination and multiple kernel learning for object tracking. In: Computer vision (ACCV 2010). Springer, Berlin, pp 511–522

  2. Kim J, Scott CD (2010) L2 kernel classification. IEEE Trans Pattern Anal Mach Intell 32:1822–1831

    Article  Google Scholar 

  3. He R et al (2011) A regularized correntropy framework for robust pattern recognition. Neural Comput 23:2074–2100

    Article  MATH  Google Scholar 

  4. Shen C et al (2007) Fast global kernel density mode seeking: applications to localization and tracking. IEEE Trans Image Process 16:1457–1469

    Article  MathSciNet  Google Scholar 

  5. Tzortzis GF, Likas C (2009) The global kernel-means algorithm for clustering in feature space. IEEE Trans Neural Netw 20:1181–1194

    Article  Google Scholar 

  6. Jorstad A et al (2011) A deformation and lighting insensitive metric for face recognition based on dense correspondences. In: 2011 IEEE conference on computer vision and pattern recognition (CVPR), pp 2353–2360

  7. Gao S et al (2010) Kernel sparse representation for image classification and face recognition. In: Computer vision (ECCV 2010). Springer, Berlin, pp 1–14

  8. Jose C et al (2013) Local deep kernel learning for efficient non-linear SVM prediction. In: Proceedings of the 30th international conference on machine learning (ICML-13), pp 486–494

  9. Caputo B et al (2004) Object categorization via local kernels. In: Proceedings of the 17th international conference on pattern recognition, 2004 (ICPR 2004), pp 132–135

  10. Boughorbel S et al (2005) Conditionally positive definite kernels for SVM based image recognition. In: IEEE international conference on multimedia and expo, 2005 (ICME 2005), pp 113–116

  11. Shen C et al (2007) Fast global kernel density mode seeking: applications to localization and tracking. IEEE Trans Image Process 16:1457–1469

    Article  MathSciNet  Google Scholar 

  12. Tzortzis G, Likas A (2008) The global kernel k-means clustering algorithm. In: IEEE international joint conference on neural networks, 2008 (IJCNN 2008). IEEE World Congress on Computational Intelligence, pp 1977–1984

  13. Gönen M, Alpaydin E (2008) Localized multiple kernel learning. In: Proceedings of the 25th international conference on machine learning, pp 352–359

  14. Rakotomamonjy A et al (2008) SimpleMKL. J Mach Learn Res 9:2491–2521

    MathSciNet  MATH  Google Scholar 

  15. Kloft M et al (2011) Lp-norm multiple kernel learning. J Mach Learn Res 12:953–997

    MathSciNet  MATH  Google Scholar 

  16. Bai L et al (2015) A quantum Jensen–Shannon graph kernel for unattributed graphs. Pattern Recognit 48:344–355

    Article  Google Scholar 

  17. Bai L, Hancock ER (2013) Graph kernels from the Jensen–Shannon divergence. J Math Imaging Vis 47:60–69

    Article  MATH  Google Scholar 

  18. Tuytelaars T et al (2011) The NBNN kernel. In: 2011 IEEE international conference on computer vision (ICCV), pp 1824–1831

  19. Zhang D et al (2010) Gaussian ERP kernel classifier for pulse waveforms classification. In: 20th international conference on pattern recognition 2010 (ICPR 10), pp 2736–2739

  20. Liu Z et al (2013) Multi-fault classification based on wavelet SVM with PSO algorithm to analyze vibration signals from rolling element bearings. Neurocomputing 99:399–410

    Article  Google Scholar 

  21. Rossi L et al (2013) A continuous-time quantum walk kernel for unattributed graphs. In: Graph-based representations in pattern recognition. Springer, Berlin, pp 101–110

  22. Luo Y et al (2013) Multiview vector-valued manifold regularization for multilabel image classification. IEEE Trans Neural Netw Learn Syst 24:709–722

    Article  Google Scholar 

  23. Luo Y et al (2013) Manifold regularized multitask learning for semi-supervised multilabel image classification. IEEE Trans Image Process 22:523–536

    Article  MathSciNet  Google Scholar 

  24. Yu J et al (2012) Semisupervised multiview distance metric learning for cartoon synthesis. IEEE Trans Image Process 21:4636–4648

    Article  MathSciNet  Google Scholar 

  25. Xu L et al (2015) An efficient multiple kernel learning in reproducing kernel Hilbert spaces (RKHS). Int J Wavelets Multiresolut Inf Process

  26. Xu L et al (2015) A local–global mixed kernel with reproducing property. Neurocomputing 168:190–199

    Article  Google Scholar 

  27. Yu J et al (2014) Click prediction for web image reranking using multimodal sparse coding

  28. Xu C et al (2014) Large-margin multi-view information bottleneck. IEEE Trans Pattern Anal Mach Intell 36:1559–1572

    Article  Google Scholar 

  29. Yu J et al (2014) High-order distance-based multiview stochastic learning in image classification

  30. Liu W, Tao D (2013) Multiview hessian regularization for image annotation. IEEE Trans Image Process 22:2676–2687

    Article  MathSciNet  Google Scholar 

  31. Xu C et al (2015) Multi-view intact space learning. IEEE Trans Pattern Anal Mach Intell 

  32. Luo Y et al (2015) Multi-view matrix completion for multi-label image classification. IEEE Trans Image Process 24:2355–2368

  33. Vito ED et al (2010) Spectral regularization for support estimation. In: Advances in neural information processing systems, pp 487–495

  34. Chapelle O et al (1999) Support vector machines for histogram-based image classification. IEEE Trans Neural Netw 10:1055–1064

    Article  Google Scholar 

  35. Aronszajn N (1950) Theory of reproducing kernels. Trans Am Math Soc 68:337–404

    Article  MathSciNet  MATH  Google Scholar 

  36. Tao D et al (2006) Asymmetric bagging and random subspace for support vector machines-based relevance feedback in image retrieval. IEEE Trans Pattern Anal Mach Intell 28:1088–1099

    Article  Google Scholar 

  37. Shawe-Taylor J, Cristianini N (2004) Kernel methods for pattern analysis. Cambridge University Press, London

  38. Lapidus L, Pinder GF (2011) Numerical solution of partial differential equations in science and engineering. Wiley, New York

  39. Ding L (2009) L1-norm and L2-norm neuroimaging methods in reconstructing extended cortical sources from EEG. In: Annual international conference of the IEEE on engineering in medicine and biology society, 2009 (EMBC 2009), pp 1922–1925

  40. Bektaş S, Şişman Y (2010) The comparison of L1 and L2-norm minimization methods. Int J Phys Sci

  41. Yi H et al (2013) Reconstruction algorithms based on l1-norm and l2-norm for two imaging models of fluorescence molecular tomography: a comparative study. J Biomed Opt 18:056013–056014

    Article  Google Scholar 

  42. Drucker H et al (1997) Support vector regression machines. Adv Neural Inf Process Syst 9:155–161

    Google Scholar 

  43. Chang C-C, Lin C-J (2011) LIBSVM: a library for support vector machines. ACM Trans Intell Syst Technol 2:27

  44. Cheng J et al (2013) Superpixel classification based optic disc and optic cup segmentation for glaucoma screening. IEEE Trans Med Imaging 32:1019–1032

    Article  Google Scholar 

Download references

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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