Learning Spectral Graph Segmentation
Abstract
We present a general graph learning algorithm for spectral graph partitioning, that allows direct supervised learning of graph structures using hand labeled training examples. 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 eigenvectors 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.
Cite
Text
Cour et al. "Learning Spectral Graph Segmentation." Proceedings of the Tenth International Workshop on Artificial Intelligence and Statistics, 2005.Markdown
[Cour et al. "Learning Spectral Graph Segmentation." Proceedings of the Tenth International Workshop on Artificial Intelligence and Statistics, 2005.](https://mlanthology.org/aistats/2005/cour2005aistats-learning/)BibTeX
@inproceedings{cour2005aistats-learning,
title = {{Learning Spectral Graph Segmentation}},
author = {Cour, Timothée and Gogin, Nicolas and Shi, Jianbo},
booktitle = {Proceedings of the Tenth International Workshop on Artificial Intelligence and Statistics},
year = {2005},
pages = {65-72},
volume = {R5},
url = {https://mlanthology.org/aistats/2005/cour2005aistats-learning/}
}