A Simple and Strongly-Local Flow-Based Method for Cut Improvement
Abstract
Many graph-based learning problems can be cast as finding a good set of vertices nearby a seed set, and a powerful methodology for these problems is based on maximum flows. We introduce and analyze a new method for locally-biased graph-based learning called SimpleLocal, which finds good conductance cuts near a set of seed vertices. An important feature of our algorithm is that it is strongly-local, meaning it does not need to explore the entire graph to find cuts that are locally optimal. This method solves the same objective as existing strongly-local flow-based methods, but it enables a simple implementation. We also show how it achieves localization through an implicit L1-norm penalty term. As a flow-based method, our algorithm exhibits several ad- vantages in terms of cut optimality and accurate identification of target regions in a graph. We demonstrate the power of SimpleLocal by solving problems on a 467 million edge graph based on an MRI scan.
Keywords
Cite
@article{arxiv.1605.08490,
title = {A Simple and Strongly-Local Flow-Based Method for Cut Improvement},
author = {Nate Veldt and David F. Gleich and Michael W. Mahoney},
journal= {arXiv preprint arXiv:1605.08490},
year = {2016}
}