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We consider a fundamental matrix completion problem where we are given an incomplete matrix and a set of constraints modeled as a CSP instance. The goal is to complete the matrix subject to the input constraints and in such a way that the complete matrix can be clustered into few subspaces with low rank. This problem generalizes several problems in data mining and machine learning, including the problem of completing a matrix into one with minimum rank. In addition to its ubiquitousdoi:10.1609/aaai.v34i04.5804 fatcat:igkdu27ydzcpjmppd5rrms266i