## Abstract

We propose a family of attributed graph kernels based on mutual
information measures, i.e., the Jensen-Tsallis (JT) q-differences (for *q*
∈ [1,2]) between probability distributions over the graphs. To this end,
we first assign a probability to each vertex of the graph through a
continuous-time quantum walk (CTQW). We then adopt the tree-index
approach [1] to strengthen the original vertex labels, and we show how
the CTQW can induce a probability distribution over these strengthened
labels. We show that our JT kernel (for *q*
= 1) overcomes the shortcoming of discarding non-isomorphic
substructures arising in the R-convolution kernels. Moreover, we prove
that the proposed JT kernels generalize the Jensen-Shannon graph kernel
[2] (for *q* = 1) and the classical subtree kernel [3] (for *q* = 2), respectively. Experimental evaluations demonstrate the effectiveness and efficiency of the JT kernels.

Original language | English |
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Title of host publication | Machine Learning and Knowledge Discovery in Databases |

Subtitle of host publication | European Conference, ECML PKDD 2014, Nancy, France, September 15-19, 2014. Proceedings |

Editors | Toon Calders, Floriana Esposito, Eyke Hüllermeier, Rosa Meo |

Place of Publication | Berlin (DE) |

Publisher | Springer |

Pages | 99-114 |

Number of pages | 16 |

ISBN (Electronic) | 978-3-662-44848-9 |

ISBN (Print) | 978-3-662-44847-2 |

DOIs | |

Publication status | Published - 31 Dec 2014 |

Event | European Conference on Machine Learning and Knowledge Discovery in Databases - Nancy, France Duration: 15 Sept 2014 → 19 Sept 2014 |

### Publication series

Name | Lecture notes in computer science |
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Publisher | Springer |

Volume | 8724 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | European Conference on Machine Learning and Knowledge Discovery in Databases |
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Abbreviated title | ECML PKDD 2014 |

Country/Territory | France |

City | Nancy |

Period | 15/09/14 → 19/09/14 |

## Keywords

- continuous-time quantum walk
- Graph kernels
- Jensen-Tsallis q-differences
- tree-index method

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