Differences
This shows you the differences between two versions of the page.
|
research [2019/03/20 09:59] |
research [2019/10/24 11:37] |
||
|---|---|---|---|
| Line 11: | Line 11: | ||
| **Parameter learning.** We study how weights for geometric diffusion that parametrize the adaptivity of the assignment flow can be learned from data. Symplectic integration ensures the commutativity of discretisation and optimisation operations. We currently investigate this approach in connection with more general objective functions. | **Parameter learning.** We study how weights for geometric diffusion that parametrize the adaptivity of the assignment flow can be learned from data. Symplectic integration ensures the commutativity of discretisation and optimisation operations. We currently investigate this approach in connection with more general objective functions. | ||
| - | * [[https://ipa.math.uni-heidelberg.de/dokuwiki/Papers/Huhnerbein2019aa.pdf|Learning Adaptive Regularization for Image Labeling Using Geometric Assignment, SSVM 2019]]. | + | * [[https://arxiv.org/abs/1910.09976|Learning Adaptive Regularization for Image Labeling Using Geometric Assignment, preprint: arXiv:1910.09976]] |
| + | * [[https://ipa.math.uni-heidelberg.de/dokuwiki/Papers/Huhnerbein2019aa.pdf|Conference version, SSVM 2019]]. | ||
| **Unsupervised label learning.** Our recent work concerns the emergence of labels in a completely unsupervised way by data //self//-assignment. The resulting unsupervised assignment flow has connections to low-rank matrix factorisation and discrete optimal mass transport that are explored in our current work. | **Unsupervised label learning.** Our recent work concerns the emergence of labels in a completely unsupervised way by data //self//-assignment. The resulting unsupervised assignment flow has connections to low-rank matrix factorisation and discrete optimal mass transport that are explored in our current work. | ||
| * [[https://ipa.math.uni-heidelberg.de/dokuwiki/Papers/Zisler2019aa.pdf|Unsupervised Labeling by Geometric and Spatially Regularized Self-Assignment, SSVM 2019]]. | * [[https://ipa.math.uni-heidelberg.de/dokuwiki/Papers/Zisler2019aa.pdf|Unsupervised Labeling by Geometric and Spatially Regularized Self-Assignment, SSVM 2019]]. | ||
| - | We extended the assignment flow to //unsupervised// scenarios, where label evolution on a feature manifold is simultaneously performed together with label assignment to given data. This paper sketches a special instance of a more general framework, the //unsupervised assignment flow//, to be introduced in a forthcoming report. | + | We extended the assignment flow to //unsupervised// scenarios, where label evolution on a feature manifold is simultaneously performed together with label assignment to given data. The following papers introduce the corresponding //unsupervised assignment flow//. |
| + | * [[https://ipa.math.uni-heidelberg.de/dokuwiki/Papers/Zern2019aa.pdf|Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment, preprint: arXiv:1904.10863]] | ||
| * [[https://ipa.math.uni-heidelberg.de/dokuwiki/Papers/gcpr2018.pdf|Unsupervised Label Learning on Manifolds by Spatially Regularized Geometric Assignment, GCPR 2018]]. | * [[https://ipa.math.uni-heidelberg.de/dokuwiki/Papers/gcpr2018.pdf|Unsupervised Label Learning on Manifolds by Spatially Regularized Geometric Assignment, GCPR 2018]]. | ||
| **Geometric numerical integration.** We conducted a comprehensive study of //geometric integration// techniques, including automatic step size adaption, for numerically computing the assignment flow in a stable, efficient and parameter-free way. | **Geometric numerical integration.** We conducted a comprehensive study of //geometric integration// techniques, including automatic step size adaption, for numerically computing the assignment flow in a stable, efficient and parameter-free way. | ||
| - | * [[https://ipa.math.uni-heidelberg.de/dokuwiki/Papers/Zeilmann2018aa.pdf|Geometric Numerical Integration of the Assignment Flow, preprint: arXiv:1810.06970]] | + | * [[https://iopscience.iop.org/article/10.1088/1361-6420/ab2772|Geometric Numerical Integration of the Assignment Flow, Inverse Problems, 2019]] |
| + | * [[https://ipa.math.uni-heidelberg.de/dokuwiki/Papers/Zeilmann2018aa.pdf|preprint: arXiv:1810.06970]] | ||
| **Evaluation of discrete graphical models.** We applied our approach to solve in a novel way the //MAP labeling problem// based on a given graphical model by smoothly combining a geometric reformulation of the local polytope relaxation with rounding to an integral solution. A key ingredient are local `//Wasserstein messages//' that couple local assignment measures along edges. | **Evaluation of discrete graphical models.** We applied our approach to solve in a novel way the //MAP labeling problem// based on a given graphical model by smoothly combining a geometric reformulation of the local polytope relaxation with rounding to an integral solution. A key ingredient are local `//Wasserstein messages//' that couple local assignment measures along edges. | ||
| - | * [[https://epubs.siam.org/doi/abs/10.1137/17M1150669|Image Labeling Based on Graphical Models Using Wasserstein Messages and Geometric Assignment, SIAM J. on Imaging Science, 11/2 (2018) 1317--1362]] | + | * [[https://epubs.siam.org/doi/abs/10.1137/17M1150669|Image Labeling Based on Graphical Models Using Wasserstein Messages and Geometric Assignment, SIAM J. on Imaging Science 11/2 (2018) 1317--1362]] |
| **Kick-off paper** that introduces the basic approach: | **Kick-off paper** that introduces the basic approach: | ||