Multiclass Diffuse Interface Models for Semi-Supervised Learning on Graphs

Start: 11/07/2012 - 1:15pm
End  : 11/07/2012 - 2:15pm

Applied Math Seminar

Cristina Garcia Cardona (CGU,SDSU)


We propose an extension 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 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
vertices of the graph (learning on graphs) with the Ginzburg-Landau
energy providing a framework to evaluate the quality of data
segmentation. The multiclass extension modifies this Ginzburg-Landau
energy functional to remove the prejudicial effect that the order of
the labelings, given by integer values, may have in the smoothing term
of the diffuse interface model. We show that the new formulation can
be used to obtain a simultaneous segmentation into several classes and
evaluate its performance in synthetic as well as real data sets. We
discuss practical aspects to improve the performance of the model and
delineate future work.

KRV 164

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