B-Matching for Spectral Clustering

Abstract. We propose preprocessing spectral clustering with b-matching to remove spurious edges in the adjacency graph prior to clustering. B-matching is a generalization of traditional maximum weight matching and is solvable in polynomial time. Instead of a permutation matrix, it produces a binary matrix with rows and columns summing to a positive integer b. The b-matching procedure prunes graph edges such that the in-degree and out-degree of each node is b, producing a more balanced variant of k-nearest-neighbor. The combinatorial algorithm optimally solves for the maximum weight subgraph and makes subsequent spectral clustering more stable and accurate. Experiments on standard datasets, visualizations, and video data support the use of b-matching to prune graphs prior to spectral clustering.