Self-Assignment Flows for Unsupervised Data Labeling on Graphs

• Main Authors: Zisler, Matthias, Zern, Artjom, Petra, Stefania, Schnörr, Christoph
• Format: Journal Article
• Language: English
• Published: 08.11.2019
• Subjects: Computer Science - Computer Vision and Pattern Recognition; Computer Science - Learning
• DOI: 10.48550/arxiv.1911.03472

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.