Topological Distances Between Brain Networks

• Published in: Connectomics in NeuroImaging Vol. 10511; pp. 161 - 170
• Main Authors: Chung, Moo K., Lee, Hyekyoung, Solo, Victor, Davidson, Richard J., Pollak, Seth D.
• Format: Book Chapter Journal Article
• Language: English
• Published: Switzerland Springer International Publishing AG 01.09.2017; Springer International Publishing
• Series: Lecture Notes in Computer Science
• ISBN: 3319671588; 9783319671581
• ISSN: 0302-9743; 1611-3349; 1611-3349
• DOI: 10.1007/978-3-319-67159-8_19

Many existing brain network distances are based on matrix norms. The element-wise differences may fail to capture underlying topological differences. Further, matrix norms are sensitive to outliers. A few extreme edge weights may severely affect the distance. Thus it is necessary to develop network distances that recognize topology. In this paper, we introduce Gromov-Hausdorff (GH) and Kolmogorov-Smirnov (KS) distances. GH-distance is often used in persistent homology based brain network models. The superior performance of KS-distance is contrasted against matrix norms and GH-distance in random network simulations with the ground truths. The KS-distance is then applied in characterizing the multimodal MRI and DTI study of maltreated children.