Unsupervised data labeling on graphs by self-assignment flows
This paper extends the recently introduced assignment flow approach for supervised image labeling to unsupervised scenarios where no labels are given. The resulting self-assignment flow takes a pairwise data affinity matrix as input data and maximizes the correlation with a low-rank matrix that is p...
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| Main Authors: | , , , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2021
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| In: |
Proceedings in applied mathematics and mechanics
Year: 2021, Volume: 20, Issue: 1, Pages: 1-2 |
| ISSN: | 1617-7061 |
| DOI: | 10.1002/pamm.202000156 |
| Online Access: | Verlag, kostenfrei, Volltext: https://doi.org/10.1002/pamm.202000156 Verlag, kostenfrei, Volltext: https://onlinelibrary.wiley.com/doi/abs/10.1002/pamm.202000156 
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| Author Notes: | Matthias Zisler, Artjom Zern, Bastian Boll, Stefania Petra, and Christoph Schnörr |
| Summary: | This paper extends the recently introduced assignment flow approach for supervised image labeling to unsupervised scenarios where no labels are given. The resulting self-assignment flow takes a pairwise data affinity matrix as input data and maximizes the correlation with a low-rank matrix that is parametrized by the variables of the assignment flow, which entails an assignment of the data to themselves through the formation of latent labels (feature prototypes). A single user parameter, the neighborhood size for the geometric regularization of assignments, drives the entire process. By smooth geodesic interpolation between different normalizations of self-assignment matrices on the positive definite matrix manifold, a one-parameter family of self-assignment flows is defined. Accordingly, our approach can be characterized from different viewpoints, e.g. as performing spatially regularized, rank-constrained discrete optimal transport, or as computing spatially regularized normalized spectral cuts. Regarding combinatorial optimization, our approach successfully determines completely positive factorizations of self-assignments in large-scale scenarios, subject to spatial regularization. Various experiments including the unsupervised learning of patch dictionaries using a locally invariant distance function, illustrate the properties of the approach. |
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| Item Description: | First published: 25 January 2021 Gesehen am 18.09.2021 |
| Physical Description: | Online Resource |
| ISSN: | 1617-7061 |
| DOI: | 10.1002/pamm.202000156 |