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Imaging Sci."],"published-print":{"date-parts":[[2020,1]]},"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.1137\/19m1298639","type":"journal-article","created":{"date-parts":[[2020,7,8]],"date-time":"2020-07-08T11:25:02Z","timestamp":1594207502000},"page":"1113-1156","source":"Crossref","is-referenced-by-count":6,"title":["Self-Assignment Flows for Unsupervised Data Labeling on Graphs"],"prefix":"10.1137","volume":"13","author":[{"given":"Matthias","family":"Zisler","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Artjom","family":"Zern","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Stefania","family":"Petra","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christoph","family":"Schn\u00f6rr","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2020,7,8]]},"reference":[{"key":"atypb1","doi-asserted-by":"crossref","unstructured":"P.A. 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