Discrete Calculus - Applied Analysis on Graphs for Computational Science

By Leo J. Grady, Jonathan R. Polimeni. 2010

371 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Computer Networks and Communications, Signal Processing

View Paper: https://www.semanticscholar.org/paper/e00553cac4b754a55609c95007b3265d602ea677

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In Computer Networks and Communications

In Signal Processing

Citations in the corpus

What are higher-order networks? (2021, methodology): “To understand why this is the case, it is insightful to introduce the Hodgedecomposition [126, 187, 251].”
EEG Emotion Recognition Using Dynamical Graph Convolutional Neural Networks (2020, methodology): “The commonly used methods to determine the entries w ij of the adjacency matrix W include the distance function method [46] and K-nearest neighbor (KNN) rule method [47].”
Graph Based Convolutional Neural Network (2016, methodology): “convolutional network in the spatially irregular domain are expansive, however the graph convolution and pooling is not trivial, with graph representations of data being the topic of ongoing research [5,21]. The use of graph representation of data for deep learning is introduced by [3], utilizing th”
Power Watershed: A Unifying Graph-Based Optimization Framework (2011, background): “Therefore, the framework of [80], which we now extend, may be seen as presenting similar ideas deﬁned on an arbitrary graph, using the bridge between continuous PDEs and graph theory provided by discrete calculus [42].”
Learning to segment under various forms of weak supervision (2015, background): “[4, 1, 2] If A is totally unimodular and b is integral, then solving linear programs of form {min cx | Ax = b,x ≥ 0} have integral optima, for any c.”
Random Walks on Simplicial Complexes and the normalized Hodge Laplacian (2018, background): “The normalized Hodge Laplacian we consider here is of a ``standard form"" [62, 68] and admits a (normalized) Hodge decomposition, which is of interest for our applications.”
Lazy Random Walks for Superpixel Segmentation (2014, methodology): “We refer the interested reader to a recent book by Grady and Polimeni [26] for more about the RW algorithm by discrete calculus.”