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  • 2020-2024  (2)
  • 2024  (2)
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  • 2020-2024  (2)
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  • 1
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    Manifold GCN: Diffusion-based Convolutional Neural Network for Manifold-valued Graphs (2024)
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    Publication Date: 2024-03-22
    Description: We propose two graph neural network layers for graphs with features in a Riemannian manifold. First, based on a manifold-valued graph diffusion equation, we construct a diffusion layer that can be applied to an arbitrary number of nodes and graph connectivity patterns. Second, we model a tangent multilayer perceptron by transferring ideas from the vector neuron framework to our general setting. Both layers are equivariant with respect to node permutations and isometries of the feature manifold. These properties have been shown to lead to a beneficial inductive bias in many deep learning tasks. Numerical examples on synthetic data as well as on triangle meshes of the right hippocampus to classify Alzheimer's disease demonstrate the very good performance of our layers.
    Language: English
    Type: article , doc-type:article
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  • 2
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    De Casteljau's Algorithm in Geometric Data Analysis: Theory and Application (2024)
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    Publication Date: 2024-04-16
    Description: For decades, de Casteljau's algorithm has been used as a fundamental building block in curve and surface design and has found a wide range of applications in fields such as scientific computing, and discrete geometry to name but a few. With increasing interest in nonlinear data science, its constructive approach has been shown to provide a principled way to generalize parametric smooth curves to manifolds. These curves have found remarkable new applications in the analysis of parameter-dependent, geometric data. This article provides a survey of the recent theoretical developments in this exciting area as well as its applications in fields such as geometric morphometrics and longitudinal data analysis in medicine, archaeology, and meteorology.
    Language: English
    Type: article , doc-type:article
    Library Location Call Number Volume/Issue/Year Availability
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    OPUS
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