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Abstract: We describe a new algorithm, termed subspace evolution and transfer SET,for solving low-rank matrix completion problems. The algorithm takes as itsinput a subset of entries of a low-rank matrix, and outputs one low-rank matrixconsistent with the given observations. The completion task is accomplished bysearching for a column space on the Grassmann manifold that matches theincomplete observations. The SET algorithm consists of two parts - subspaceevolution and subspace transfer. In the evolution part, we use a gradientdescent method on the Grassmann manifold to refine our estimate of the columnspace. Since the gradient descent algorithm is not guaranteed to converge, dueto the existence of barriers along the search path, we design a new mechanismfor detecting barriers and transferring the estimated column space across thebarriers. This mechanism constitutes the core of the transfer step of thealgorithm. The SET algorithm exhibits excellent empirical performance for bothhigh and low sampling rate regimes.



Author: Wei Dai, Olgica Milenkovic, Ely Kerman

Source: https://arxiv.org/







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