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Since the columns belong to a union of subspaces, the problem may be viewed as a missing-data version of the subspace clustering problem. Let X {\displaystyle X} be an n × N {\displaystyle n\times N} matrix whose (complete) columns lie in a union of at most k {\displaystyle k} subspaces, each of r a n k ≤ r < n {\displaystyle rank\leq r<n ...