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Center for Nonlinear Studies |
We propose generalizations of a binary diffuse interface model for graph segmentation to the case of multiple classes. The original binary diffuse interface model adapts the Ginzburg-Landau (GL) continuum energy functional to a semi-supervised setup on graphs. The graph structure is used to encode a measure of similarity between data points. A small sample of labeled data points (semi-supervised) serves as seeds from which label information can be propagated throughout the graph structure. In this way, the problem can be posed as a function estimation over the nodes of the graph (learning on graphs) with the GL energy providing a framework to evaluate the quality of data segmentation. We develop two multiclass generalizations, one based on a scalar representation and other based on a vector-field representation. We compare the performance of the two multiclass formulations in synthetic data as well as real benchmark sets. The experimental results demonstrate that our methods are competitive with the state-of-the-art among other graph-based algorithms.
Host: Brendt Wohlberg