Geometric numerical integration of the assignment flow
The assignment flow is a smooth dynamical system that evolves on an elementary statistical manifold and performs contextual data labeling on a graph. We derive and introduce the linear assignment flow that evolves nonlinearly on the manifold, but is governed by a linear ODE on the tangent space. Var...
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| Main Authors: | , , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
20 February 2020
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| In: |
Inverse problems
Year: 2020, Volume: 36, Issue: 3 |
| ISSN: | 1361-6420 |
| DOI: | 10.1088/1361-6420/ab2772 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1088/1361-6420/ab2772 Verlag, lizenzpflichtig, Volltext: https://iopscience.iop.org/article/10.1088/1361-6420/ab2772 
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| Author Notes: | Alexander Zeilmann, Fabrizio Savarino, Stefania Petra and Christoph Schnörr |
| Summary: | The assignment flow is a smooth dynamical system that evolves on an elementary statistical manifold and performs contextual data labeling on a graph. We derive and introduce the linear assignment flow that evolves nonlinearly on the manifold, but is governed by a linear ODE on the tangent space. Various numerical schemes adapted to the mathematical structure of these two models are designed and studied, for the geometric numerical integration of both flows: embedded Runge-Kutta-Munthe-Kaas schemes for the nonlinear flow, adaptive Runge-Kutta schemes and exponential integrators for the linear flow. All algorithms are parameter free, except for setting a tolerance value that specifies adaptive step size selection by monitoring the local integration error, or fixing the dimension of the Krylov subspace approximation. These algorithms provide a basis for applying the assignment flow to machine learning scenarios beyond supervised labeling, including unsupervised labeling and learning from controlled assignment flows. |
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| Item Description: | Gesehen am 25.03.2021 |
| Physical Description: | Online Resource |
| ISSN: | 1361-6420 |
| DOI: | 10.1088/1361-6420/ab2772 |