Departmental Papers (CIS)

Learning Spectral Graph Segmentation

Jianbo Shi, University of Pennsylvania
Timothee Cour, University of Pennsylvania
Nicolas Gogin, Ecole Polytechnique

Document Type Conference Paper

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Abstract

We present a general graph learning algo- rithm for spectral graph partitioning, that allows direct supervised learning of graph structures using hand labeled training exam- ples. The learning algorithm is based on gradient descent in the space of all feasible graph weights. Computation of the gradient involves finding the derivatives of eigenvec- tors with respect to the graph weight matrix. We show the derivatives of eigenvectors exist and can be computed in an exact analytical form using the theory of implicit functions. Furthermore, we show for a simple case, the gradient converges exponentially fast. In the image segmentation domain, we demonstrate how to encode top-down high level object prior in a bottom-up shape detection process.

 

Date Posted: 17 July 2012