Matrix rank minimization problem is in general NP-hard. The nuclear norm isused to substitute the rank function in many recent studies. Nevertheless, thenuclear norm approximation adds all singular values together and theapproximation error may depend heavily on the magnitudes of singular values.This might restrict its capability in dealing with many practical problems. Inthis paper, an arctangent function is used as a tighter approximation to therank function. We use it on the challenging subspace clustering problem. Forthis nonconvex minimization problem, we develop an effective optimizationprocedure based on a type of augmented Lagrange multipliers (ALM) method.Extensive experiments on face clustering and motion segmentation show that theproposed method is effective for rank approximation.
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