On the Continuity of Moore-Penrose Inverse of the Graph Laplacian

Graph Laplacian is a fundamental tool in various fields such as spectral clustering, network analysis, image processing, and, deep learning recently for studying message passing in graph neural network models. To support the theoretical use of the graph Laplacian in these fields, in this work, we st...

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Bibliographic Details
Main Authors: Lin, Tse-Yu, Tsai, Yen-lung
Format: Conference Proceeding
Language:English
Subjects:
Analytical models
Consumer electronics
continuity
Deep learning
graph connectivity
graph Laplacian
Graph neural networks
Image processing
Laplace equations
Message passing
Moore-Penrose inverse
Network analyzers
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Summary:Graph Laplacian is a fundamental tool in various fields such as spectral clustering, network analysis, image processing, and, deep learning recently for studying message passing in graph neural network models. To support the theoretical use of the graph Laplacian in these fields, in this work, we study the continuity of the Moore-Penrose generalized inverse of the graph Laplacian. We provide a graph-theoretical proof of this continuity in terms of the connectivity of the underlying graph associated with a given graph Laplacian matrix.
ISSN:2693-0854
DOI:10.1109/GCCE62371.2024.10760335