## Expressivity versus efficiency of graph kernels (2003)

Venue: | Proceedings of the First International Workshop on Mining Graphs, Trees and Sequences |

Citations: | 37 - 0 self |

### BibTeX

@INPROCEEDINGS{Ramon03expressivityversus,

author = {Jan Ramon and Thomas Gärtner},

title = {Expressivity versus efficiency of graph kernels},

booktitle = {Proceedings of the First International Workshop on Mining Graphs, Trees and Sequences},

year = {2003},

pages = {65--74}

}

### Years of Citing Articles

### OpenURL

### Abstract

Abstract. Recently, kernel methods have become a popular tool for machine learning and data mining. As most ‘real-world ’ data is structured, research in kernel methods has begun investigating kernels for various kinds of structured data. One of the most widely used tools for modeling structured data are graphs. In this paper we study the trade-off between expressivity and efficiency of graph kernels. First, we motivate the need for this discussion by showing that fully general graph kernels can not even be approximated efficiently. We also discuss generalizations of graph kernels defined in literature and show that they are either not positive definite or not very useful. Finally, we propose a new graph kernel based on subtree patterns. We argue that while a little more computationally expensive, this kernel is more expressive than kernels based on walks. 1

### Citations

2145 | Learning with kernels
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(Show Context)
Citation Context ...on Support vector machines [1] are among the most successful recent developments within the machine learning community. Along with some other learning algorithms they form the class of kernel methods =-=[10]-=-. The computational attractiveness of kernel methods is due to the fact that they can be applied in high dimensional feature spaces without suffering from the high cost of explicitly computing the fea... |

1373 | A training algorithm for optimal margin classifiers
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Citation Context ...graph kernel based on subtree patterns. We argue that while a little more computationally expensive, this kernel is more expressive than kernels based on walks. 1 Introduction Support vector machines =-=[1]-=- are among the most successful recent developments within the machine learning community. Along with some other learning algorithms they form the class of kernel methods [10]. The computational attrac... |

735 |
Graph Theory
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- 1997
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Citation Context ...irst review a few basic definitions and introduce some notations that will be used in the sequel of this paper. For a more in-depth discussion of graphs and related concepts the reader is referred to =-=[3, 8]-=-. Labeled directed graphs Generally, a graph G is described by a finite set of vertices V, a finite set of edges E. Therefore, a graph is commonly denoted G(V, E). For labeled graphs there is addition... |

400 | Text classification using string kernels
- Lodhi, Shawe-taylor, et al.
- 2002
(Show Context)
Citation Context ...ons for graphs has proven difficult. In order to control the complexity of such kernels, one line of existing research has concentrated on special kinds of graphs, in particular, trees [2] or strings =-=[11, 9]-=- which results in efficient kernels, but loses most of the power of general graphs. Others [4, 7] have investigated efficient kernels for general graphs based on particular kinds of walks, which captu... |

271 | Convolution kernels for natural language
- Collins, Duffy
- 2002
(Show Context)
Citation Context ...e kernel functions for graphs has proven difficult. In order to control the complexity of such kernels, one line of existing research has concentrated on special kinds of graphs, in particular, trees =-=[2]-=- or strings [11, 9] which results in efficient kernels, but loses most of the power of general graphs. Others [4, 7] have investigated efficient kernels for general graphs based on particular kinds of... |

199 |
Combinatorial Optimization - Theory and Algorithms; Second Edition
- Korte, Vygen
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(Show Context)
Citation Context ...irst review a few basic definitions and introduce some notations that will be used in the sequel of this paper. For a more in-depth discussion of graphs and related concepts the reader is referred to =-=[3, 8]-=-. Labeled directed graphs Generally, a graph G is described by a finite set of vertices V, a finite set of edges E. Therefore, a graph is commonly denoted G(V, E). For labeled graphs there is addition... |

142 | Product Graphs: Structure and Recognition - Imrich, Klavžar - 2000 |

138 | On graph kernels: Hardness results and efficient alternatives
- Gärtner, Flach, et al.
- 2003
(Show Context)
Citation Context ...aphs. Others [4, 7] have investigated efficient kernels for general graphs based on particular kinds of walks, which captures more, but still far from all of the structure of the graph.sMore recently =-=[5]-=- answered the questions whether it is possible to define kernels that take the entire structure of graphs into account. While those kernels can be defined, computing them is hard. For that reason, alt... |

26 |
Exponential and geometric kernels for graphs
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- 2002
(Show Context)
Citation Context ...of existing research has concentrated on special kinds of graphs, in particular, trees [2] or strings [11, 9] which results in efficient kernels, but loses most of the power of general graphs. Others =-=[4, 7]-=- have investigated efficient kernels for general graphs based on particular kinds of walks, which captures more, but still far from all of the structure of the graph.sMore recently [5] answered the qu... |

25 |
Kernels for graph classification
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- 2002
(Show Context)
Citation Context ...of existing research has concentrated on special kinds of graphs, in particular, trees [2] or strings [11, 9] which results in efficient kernels, but loses most of the power of general graphs. Others =-=[4, 7]-=- have investigated efficient kernels for general graphs based on particular kinds of walks, which captures more, but still far from all of the structure of the graph.sMore recently [5] answered the qu... |

20 |
Kernels from matching operations
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- 1999
(Show Context)
Citation Context ...ons for graphs has proven difficult. In order to control the complexity of such kernels, one line of existing research has concentrated on special kinds of graphs, in particular, trees [2] or strings =-=[11, 9]-=- which results in efficient kernels, but loses most of the power of general graphs. Others [4, 7] have investigated efficient kernels for general graphs based on particular kinds of walks, which captu... |