### Abstract

Dense subgraphs are fundamental patterns in graphs, and dense subgraph detection is often the key step of numerous graph mining applications. Most of the existing methods aim to find a single subgraph with a high density. However, dense subgraphs at different granularities could reveal more intriguing patterns in the underlying graph. In this paper, we propose to hierarchically detect dense subgraphs. The key idea of our method (HiDDen) is to envision the density of subgraphs as a relative measure to its background (i.e., the subgraph at the coarse granularity). Given that the hierarchical dense subgraph detection problem is essentially a nonconvex quadratic programming problem, we propose effective and efficient alternative projected gradient based algorithms to solve it. The experimental evaluations on real graphs demonstrate that (1) our proposed algorithms find subgraphs with an up to 40% higher density in almost every hierarchy; (2) the densities of different hierarchies exhibit a desirable variety across different granularities; (3) our projected gradient descent based algorithm scales linearly w.r.t the number of edges of the input graph; and (4) our methods are able to reveal interesting patterns in the underlying graphs (e.g., synthetic ID in financial fraud detection).

Original language | English (US) |
---|---|

Title of host publication | Proceedings of the 17th SIAM International Conference on Data Mining, SDM 2017 |

Publisher | Society for Industrial and Applied Mathematics Publications |

Pages | 570-578 |

Number of pages | 9 |

ISBN (Electronic) | 9781611974874 |

State | Published - 2017 |

Event | 17th SIAM International Conference on Data Mining, SDM 2017 - Houston, United States Duration: Apr 27 2017 → Apr 29 2017 |

### Other

Other | 17th SIAM International Conference on Data Mining, SDM 2017 |
---|---|

Country | United States |

City | Houston |

Period | 4/27/17 → 4/29/17 |

### Fingerprint

### Keywords

- Financial fraud detection
- Graph mining
- Hierarchical dense subgraph detection

### ASJC Scopus subject areas

- Software
- Computer Science Applications

### Cite this

*Proceedings of the 17th SIAM International Conference on Data Mining, SDM 2017*(pp. 570-578). Society for Industrial and Applied Mathematics Publications.

**HiDDen : Hierarchical dense subgraph detection with application to financial fraud detection.** / Zhang, Si; Zhou, Dawei; Yildirim, Mehmet Yigit; Alcorn, Scott; He, Jingrui; Davulcu, Hasan; Tong, Hanghang.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 17th SIAM International Conference on Data Mining, SDM 2017.*Society for Industrial and Applied Mathematics Publications, pp. 570-578, 17th SIAM International Conference on Data Mining, SDM 2017, Houston, United States, 4/27/17.

}

TY - GEN

T1 - HiDDen

T2 - Hierarchical dense subgraph detection with application to financial fraud detection

AU - Zhang, Si

AU - Zhou, Dawei

AU - Yildirim, Mehmet Yigit

AU - Alcorn, Scott

AU - He, Jingrui

AU - Davulcu, Hasan

AU - Tong, Hanghang

PY - 2017

Y1 - 2017

N2 - Dense subgraphs are fundamental patterns in graphs, and dense subgraph detection is often the key step of numerous graph mining applications. Most of the existing methods aim to find a single subgraph with a high density. However, dense subgraphs at different granularities could reveal more intriguing patterns in the underlying graph. In this paper, we propose to hierarchically detect dense subgraphs. The key idea of our method (HiDDen) is to envision the density of subgraphs as a relative measure to its background (i.e., the subgraph at the coarse granularity). Given that the hierarchical dense subgraph detection problem is essentially a nonconvex quadratic programming problem, we propose effective and efficient alternative projected gradient based algorithms to solve it. The experimental evaluations on real graphs demonstrate that (1) our proposed algorithms find subgraphs with an up to 40% higher density in almost every hierarchy; (2) the densities of different hierarchies exhibit a desirable variety across different granularities; (3) our projected gradient descent based algorithm scales linearly w.r.t the number of edges of the input graph; and (4) our methods are able to reveal interesting patterns in the underlying graphs (e.g., synthetic ID in financial fraud detection).

AB - Dense subgraphs are fundamental patterns in graphs, and dense subgraph detection is often the key step of numerous graph mining applications. Most of the existing methods aim to find a single subgraph with a high density. However, dense subgraphs at different granularities could reveal more intriguing patterns in the underlying graph. In this paper, we propose to hierarchically detect dense subgraphs. The key idea of our method (HiDDen) is to envision the density of subgraphs as a relative measure to its background (i.e., the subgraph at the coarse granularity). Given that the hierarchical dense subgraph detection problem is essentially a nonconvex quadratic programming problem, we propose effective and efficient alternative projected gradient based algorithms to solve it. The experimental evaluations on real graphs demonstrate that (1) our proposed algorithms find subgraphs with an up to 40% higher density in almost every hierarchy; (2) the densities of different hierarchies exhibit a desirable variety across different granularities; (3) our projected gradient descent based algorithm scales linearly w.r.t the number of edges of the input graph; and (4) our methods are able to reveal interesting patterns in the underlying graphs (e.g., synthetic ID in financial fraud detection).

KW - Financial fraud detection

KW - Graph mining

KW - Hierarchical dense subgraph detection

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M3 - Conference contribution

SP - 570

EP - 578

BT - Proceedings of the 17th SIAM International Conference on Data Mining, SDM 2017

PB - Society for Industrial and Applied Mathematics Publications

ER -