## Graph Edit Distance from Spectral Seriation

Robles-Kelly, Antonio; Hancock, Edwin R

### Description

This paper is concerned with computing graph edit distance. One of the criticisms that can be leveled at existing methods for computing graph edit distance is that they lack some of the formality and rigor of the computation of string edit distance. Hence, our aim is to convert graphs to string sequences so that string matching techniques can be used. To do this, we use a graph spectral seriation method to convert the adjacency matrix into a string or sequence order. We show how the serial...[Show more]

dc.contributor.author | Robles-Kelly, Antonio | |
---|---|---|

dc.contributor.author | Hancock, Edwin R | |

dc.date.accessioned | 2015-12-13T22:52:10Z | |

dc.identifier.issn | 0162-8828 | |

dc.identifier.uri | http://hdl.handle.net/1885/81444 | |

dc.description.abstract | This paper is concerned with computing graph edit distance. One of the criticisms that can be leveled at existing methods for computing graph edit distance is that they lack some of the formality and rigor of the computation of string edit distance. Hence, our aim is to convert graphs to string sequences so that string matching techniques can be used. To do this, we use a graph spectral seriation method to convert the adjacency matrix into a string or sequence order. We show how the serial ordering can be established using the leading eigenvector of the graph adjacency matrix. We pose the problem of graph-matching as a maximum a posteriori probability (MAP) alignment of the seriation sequences for pairs of graphs. This treatment leads to an expression in which the edit cost is the negative logarithm of the a posteriori sequence alignment probability. We compute the edit distance by finding the sequence of string edit operations which minimizes the cost of the path traversing the edit lattice. The edit costs are determined by the components of the leading eigenvectors of the adjacency matrix and by the edge densities of the graphs being matched. We demonstrate the utility of the edit distance on a number of graph clustering problems. | |

dc.publisher | Institute of Electrical and Electronics Engineers (IEEE Inc) | |

dc.source | IEEE Transactions on Pattern Analysis and Machine Intelligence | |

dc.source.uri | http://ieeexplore.ieee.org/iel5/34/30209/01388263.pdf?isnumber=30209=JNL&arnumber=1388263&arSt=+365&ared=+378&arAuthor=Robles-Kelly%2C+A.%3B+Hancock%2C+E.R. | |

dc.subject | Keywords: Computer graphics; Eigenvalues and eigenfunctions; Graph theory; Graphic methods; Mathematical models; Matrix algebra; Object recognition; Pattern recognition; Probability; Graph edit distance; Graph matching; Graph seriation; Graph-spectral methods; Maxi Graph edit distance; Graph seriation; Graph-spectral methods; Maximum a posteriori probability (MAP) | |

dc.title | Graph Edit Distance from Spectral Seriation | |

dc.type | Journal article | |

local.description.notes | Imported from ARIES | |

local.description.refereed | Yes | |

local.identifier.citationvolume | 27 | |

dc.date.issued | 2005 | |

local.identifier.absfor | 080109 - Pattern Recognition and Data Mining | |

local.identifier.ariespublication | MigratedxPub9735 | |

local.type.status | Published Version | |

local.contributor.affiliation | Robles-Kelly, Antonio, College of Engineering and Computer Science, ANU | |

local.contributor.affiliation | Hancock, Edwin R, University of York | |

local.description.embargo | 2037-12-31 | |

local.bibliographicCitation.issue | 3 | |

local.bibliographicCitation.startpage | 365 | |

local.bibliographicCitation.lastpage | 378 | |

dc.date.updated | 2015-12-11T10:49:29Z | |

local.identifier.scopusID | 2-s2.0-15044365894 | |

Collections | ANU Research Publications |

### Download

File | Description | Size | Format | Image |
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01_Robles-Kelly_Graph_Edit_Distance_from_2005.pdf | 1.59 MB | Adobe PDF | Request a copy |

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