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In low-rank matrix completion, researchers usually devote to solving the following problem as: begin{aligned} mathop {arg min }limits _mathbf{F}&quad mathrm{rank}(mathbf{F}) mathrm{s.t.}&quad mathbf{F}_{i,j} = y_{ij}, end{aligned}where (mathbf F) is a complete low-rank matrix and (mathbf{F}_{i,j}) is the (i, j -entry for (mathbf F).
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