Graph Partitioning by Spectral Rounding: Applications in Image Segmentation and Clustering
journal contributionposted on 1994-02-01, 00:00 authored by Gary L. Miller, David Tolliver
We introduce a new family of spectral partitioning methods. Edge separators of a graph are produced by iteratively reweighting the edges until the graph disconnects into the prescribed number of components. At each iteration a small number of eigenvectors with small eigenvalue are computed and used to determine the reweighting. In this way spectral rounding directly produces discrete solutions where as current spectral algorithms must map the continuous eigenvectors to discrete solutions by employing a heuristic geometric separator (e.g. k-means). We show that spectral rounding compares favorably to current spectral approximations on the Normalized Cut criterion (NCut). Results are given in the natural image segmentation, medical image segmentation, and clustering domains. A practical version is shown to converge.