A Mixed Entropy Local-Global Reproducing Kernel for Attributed Graphs

  • Lixin Cui
  • Lu BaiEmail author
  • Luca Rossi
  • Zhihong Zhang
  • Lixiang Xu
  • Edwin R. Hancock
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11004)


In this paper, we develop a new mixed entropy local-global reproducing kernel for vertex attributed graphs based on depth-based representations that naturally reflect both local and global entropy based graph characteristics. Specifically, for a pair of graphs, we commence by computing the nest depth-based representations rooted at the centroid vertices. The resulting mixed local-global reproducing kernel for a pair of graphs is computed by measuring a basic \(H^1\)-reproducing kernel between their nest representations associated with different entropy measures. We show that the proposed kernel not only reflect both the local and global graph characteristics through the nest depth-based representations, but also reflect rich edge connection information and vertex label information through different kinds of entropy measures. Moreover, since both the required basic \(H^1\)-reproducing kernel and the nest depth-based representation can be computed in a polynomial time, the new proposed kernel processes efficient computational complexity. Experiments on standard graph datasets demonstrate the effectiveness and efficiency of the proposed kernel.


Local-global graph kernels Attributed graphs Entropy 



This work is supported by the National Natural Science Foundation of China (Grant no. 61602535, 61503422 and 61773415), the Open Projects Program of National Laboratory of Pattern Recognition, and the program for innovation research in Central University of Finance and Economics.


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Lixin Cui
    • 1
  • Lu Bai
    • 1
    Email author
  • Luca Rossi
    • 2
  • Zhihong Zhang
    • 3
  • Lixiang Xu
    • 4
  • Edwin R. Hancock
    • 5
  1. 1.Central University of Finance and EconomicsBeijingChina
  2. 2.Aston UniversityBirminghamUK
  3. 3.Xiamen UniversityXiamenChina
  4. 4.Hefei UniversityHefeiChina
  5. 5.University of YorkYorkUK

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