## Abstract

A graph is a flexible data structure for various data, such as the Web, SNSs and molecular architectures. Not only the data expressed naturally by a graph, it is also used for data which does not have explicit graph structures by extracting implicit relationships hidden in data, e.g. co-occurrence relationships of words in text and similarity relationships of pixels of an image. By the extraction, we can make full use of many sophisticated methods for graphs to solve a wide range of problems. In analysis of graphs, the graph clustering problem is one of the most important problems, which is to divide all vertices of a given graph into some groups called clusters. Existing algorithms for the problem typically assume that the number of intra-cluster edges is large while the number of inter-cluster edges is absolutely small. Therefore these algorithms fail to do clustering in case of noisy graphs, and the extraction of implicit relationships tends to yield noisy ones because it is subject to a definition of a relation among vertices. Instead of such an assumption, we introduce a macroscopic structure (MS), which is a graph of clusters and roughly describes a structure of a given graph. This paper presents a graph clustering algorithm which, given a graph and the number of clusters, tries to find a set of clusters such that the distance between an MS induced from calculated clusters and the ideal MS for the given number of clusters is minimized. In other words, it solves the clustering problem as an optimization problem. For the m-clustering problem, the ideal MS is defined as an m-vertex graph such that each vertex has only a self-loop. To confirm the performance improvements exhaustively, we conducted experiments with artificial graphs with different amounts of noise. The results show that our method can handle very noisy graphs correctly while existing algorithms completely failed to do clustering. Furthermore, even for graphs with less noise, our algorithm treats them well if the difference between edge densities of intra-cluster edges and those of inter-cluster edges are sufficiently big. We also did experiments on graphs transformed from vector data as a more practical case. From the results we found that our algorithm, indeed, works much better on noisy graphs than the existing ones.

Original language | English |
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Title of host publication | Discovery Science - 14th International Conference, DS 2011, Proceedings |

Pages | 335-350 |

Number of pages | 16 |

DOIs | |

Publication status | Published - Oct 17 2011 |

Event | 14th International Conference on Discovery Science, DS 2011, Co-located with the 22nd International Conference on Algorithmic Learning Theory, ALT 2011 - Espoo, Finland Duration: Oct 5 2011 → Oct 7 2011 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 6926 LNAI |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 14th International Conference on Discovery Science, DS 2011, Co-located with the 22nd International Conference on Algorithmic Learning Theory, ALT 2011 |
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Country | Finland |

City | Espoo |

Period | 10/5/11 → 10/7/11 |

## All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)