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The bipartite graph structure has shown its promising ability in facilitatingthe subspace clustering and spectral clustering algorithms for large-scaledatasets. To avoid the post-processing via k-means during the bipartite graphpartitioning, the constrained Laplacian rank (CLR) is often utilized forconstraining the number of connected components (i.e., clusters) in thebipartite graph, which, however, neglects the distribution (or normalization)of these connected components and may lead to imbalanced or even ill clusters.Despite the significant success of normalized cut (Ncut) in general graphs, itremains surprisingly an open problem how to enforce a one-step normalized cutfor bipartite graphs, especially with linear-time complexity. In this paper, wefirst characterize a novel one-step bipartite graph cut (OBCut) criterion withnormalized constraints, and theoretically prove its equivalence to a tracemaximization problem. Then we extend this cut criterion to a scalable subspaceclustering approach, where adaptive anchor learning, bipartite graph learning,and one-step normalized bipartite graph partitioning are simultaneously modeledin a unified objective function, and an alternating optimization algorithm isfurther designed to solve it in linear time. Experiments on a variety ofgeneral and large-scale datasets demonstrate the effectiveness and scalabilityof our approach.

One-step Bipartite Graph Cut: A Normalized Formulation and Its Application to Scalable Subspace Clustering