
Topological and Geometric Reconstruction of Metric Graphs in R^n
We propose an algorithm to estimate the topology of an embedded metric g...
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Ordinal Pattern Kernel for Brain Connectivity Network Classification
Brain connectivity networks, which characterize the functional or struct...
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GCREWE: Graph CompREssion With Embedding for Network Alignment
Network alignment is useful for multiple applications that require incre...
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GRASP: Graph Alignment through Spectral Signatures
What is the best way to match the nodes of two graphs? This graph alignm...
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Distance Metric Learning using Graph Convolutional Networks: Application to Functional Brain Networks
Evaluating similarity between graphs is of major importance in several c...
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Spectral Graph Transformer Networks for Brain Surface Parcellation
The analysis of the brain surface modeled as a graph mesh is a challengi...
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Folding Simulation of Rigid Origami with Lagrange Multiplier Method
Origami crease patterns are folding paths that transform flat sheets int...
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Rigid Graph Alignment
Graph databases have been the subject of significant research and development. Problems such as modularity, centrality, alignment, and clustering have been formalized and solved in various application contexts. In this paper, we focus on databases for applications in which graphs have a spatial basis, which we refer to as rigid graphs. Nodes in such graphs have preferred positions relative to their graph neighbors. Examples of such graphs include abstractions of large biomolecules, functional connectomes of the human brain, and mobile device/ sensor communication logs. When analyzing such networks it is important to consider edge lengths; e.g., when identifying conserved patterns through graph alignment, it is important for conserved edges to have correlated lengths, in addition to topological similarity. In contrast to a large body of work on topological graph alignment, rigid graph alignment simultaneously aligns the network, as well as the underlying structure as characterized by edge lengths. We formulate the problem and present a metaalgorithm based on expectationmaximization that alternately aligns the network and the structure. We demonstrate that our metaalgorithm significantly improves the quality of alignments in target applications, compared to topological or structural aligners alone. We apply rigid graph alignment to functional brain networks derived from 20 subjects drawn from the Human Connectome Project (HCP) database, and show over a twofold increase in quality of alignment over state of the art topological aligners. We evaluate the impact of various parameters associated with input datasets through a study on synthetic graphs, where we fully characterize the performance of our method. Our results are broadly applicable to other applications and abstracted networks that can be embedded in metric spaces – e.g., through spectral embeddings.
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