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The K-subspaces (KSS) method is a generalization of the K-means method forsubspace clustering. In this work, we present local convergence analysis and arecovery guarantee for KSS, assuming data are generated by the semi-randomunion of subspaces model, where $N$ points are randomly sampled from $K \ge 2$overlapping subspaces. We show that if the initial assignment of the KSS methodlies within a neighborhood of a true clustering, it converges at a superlinearrate and finds the correct clustering within $\Theta(\log\log N)$ iterationswith high probability. Moreover, we propose a thresholding inner-product basedspectral method for initialization and prove that it produces a point in thisneighborhood. We also present numerical results of the studied method tosupport our theoretical developments.

Convergence and Recovery Guarantees of the K-Subspaces Method for Subspace Clustering