Riemannian Patch Assignment Gradient Flows
This addresses graph-based data labeling problems, but appears incremental as it builds on existing patch assignment and flow-based regularization methods.
The paper tackles the problem of metric data labeling on graphs by introducing patch assignment flows that regularize initial local labelings through dynamic interaction of labels and label assignments, achieving maximal consistency via Riemannian ascent flow integration. Experiments demonstrate properties including uncertainty quantification of label assignments.
This paper introduces patch assignment flows for metric data labeling on graphs. Labelings are determined by regularizing initial local labelings through the dynamic interaction of both labels and label assignments across the graph, entirely encoded by a dictionary of competing labeled patches and mediated by patch assignment variables. Maximal consistency of patch assignments is achieved by geometric numerical integration of a Riemannian ascent flow, as critical point of a Lagrangian action functional. Experiments illustrate properties of the approach, including uncertainty quantification of label assignments.