### Abstract

The difference between networks has been often assessed by the difference of global topological measures such as the clustering coefficient, degree distribution and modularity. In this paper, we introduce a new framework for measuring the network difference using the Gromov-Hausdorff (GH) distance, which is often used in shape analysis. In order to apply the GH distance, we define the shape of the brain network by piecing together the patches of locally connected nearest neighbors using the graph filtration. The shape of the network is then transformed to an algebraic form called the single linkage matrix. The single linkage matrix is subsequently used in measuring network differences using the GH distance. As an illustration, we apply the proposed framework to compare the FDG-PET based functional brain networks out of 24 attention deficit hyperactivity disorder (ADHD) children, 26 autism spectrum disorder (ASD) children and 11 pediatric control subjects.

Original language | English |
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Pages (from-to) | 302-309 |

Number of pages | 8 |

Journal | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Volume | 6892 LNCS |

Issue number | PART 2 |

DOIs | |

State | Published - 11 Oct 2011 |

Event | 14th International Conference on Medical Image Computing and Computer Assisted Intervention, MICCAI 2011 - Toronto, ON, Canada Duration: 18 Sep 2011 → 22 Sep 2011 |

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### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*,

*6892 LNCS*(PART 2), 302-309. https://doi.org/10.1007/978-3-642-23629-7_37

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*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*, vol. 6892 LNCS, no. PART 2, pp. 302-309. https://doi.org/10.1007/978-3-642-23629-7_37

**Computing the shape of brain networks using graph filtration and Gromov-Hausdorff metric.** / Lee, Hyekyoung; Chung, Moo K.; Kang, Hyejin; Kim, Boong Nyun; Lee, Dong Soo.

Research output: Contribution to journal › Conference article › Research › peer-review

TY - JOUR

T1 - Computing the shape of brain networks using graph filtration and Gromov-Hausdorff metric

AU - Lee, Hyekyoung

AU - Chung, Moo K.

AU - Kang, Hyejin

AU - Kim, Boong Nyun

AU - Lee, Dong Soo

PY - 2011/10/11

Y1 - 2011/10/11

N2 - The difference between networks has been often assessed by the difference of global topological measures such as the clustering coefficient, degree distribution and modularity. In this paper, we introduce a new framework for measuring the network difference using the Gromov-Hausdorff (GH) distance, which is often used in shape analysis. In order to apply the GH distance, we define the shape of the brain network by piecing together the patches of locally connected nearest neighbors using the graph filtration. The shape of the network is then transformed to an algebraic form called the single linkage matrix. The single linkage matrix is subsequently used in measuring network differences using the GH distance. As an illustration, we apply the proposed framework to compare the FDG-PET based functional brain networks out of 24 attention deficit hyperactivity disorder (ADHD) children, 26 autism spectrum disorder (ASD) children and 11 pediatric control subjects.

AB - The difference between networks has been often assessed by the difference of global topological measures such as the clustering coefficient, degree distribution and modularity. In this paper, we introduce a new framework for measuring the network difference using the Gromov-Hausdorff (GH) distance, which is often used in shape analysis. In order to apply the GH distance, we define the shape of the brain network by piecing together the patches of locally connected nearest neighbors using the graph filtration. The shape of the network is then transformed to an algebraic form called the single linkage matrix. The single linkage matrix is subsequently used in measuring network differences using the GH distance. As an illustration, we apply the proposed framework to compare the FDG-PET based functional brain networks out of 24 attention deficit hyperactivity disorder (ADHD) children, 26 autism spectrum disorder (ASD) children and 11 pediatric control subjects.

UR - http://www.scopus.com/inward/record.url?scp=80053504977&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-23629-7_37

DO - 10.1007/978-3-642-23629-7_37

M3 - Conference article

VL - 6892 LNCS

SP - 302

EP - 309

JO - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

JF - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SN - 0302-9743

IS - PART 2

ER -