Unsupervised data labeling on graphs by self-assignment flows

• Verfasst von: Zisler, Matthias [VerfasserIn]
• Verfasst von: Zern, Artjom [VerfasserIn]
• Verfasst von: Boll, Bastian [VerfasserIn]
• Verfasst von: Petra, Stefania [VerfasserIn]
• Verfasst von: Schnörr, Christoph [VerfasserIn]
• Titel: Unsupervised data labeling on graphs by self-assignment flows
• Verf.angabe: Matthias Zisler, Artjom Zern, Bastian Boll, Stefania Petra, and Christoph Schnörr
• Jahr: 2021
• Umfang: 2 S.
• Fussnoten: First published: 25 January 2021 ; Gesehen am 18.09.2021
• Titel Quelle: Enthalten in: Proceedings in applied mathematics and mechanics
• Ort Quelle: Weinheim [u.a.] : Wiley-VCH, 2002
• Jahr Quelle: 2021
• Band/Heft Quelle: 20(2021), 1, Artikel-ID e202000156, Seite 1-2
• ISSN Quelle: 1617-7061
• DOI: doi:10.1002/pamm.202000156
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1770926712
• K10plus-PPN:
  Universitätsbibliothek
• Lokale URL UB: Zum Volltext

Abstract

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.