Matrix rank minimizing subject to affine constraints arises in many
application areas, ranging from signal processing to machine learning. Nuclear
norm is a convex relaxation for this problem which can recover the rank exactly
under some restricted and theoretically interesting conditions...
many real-world applications, nuclear norm approximation to the rank function
can only produce a result far from the optimum. To seek a solution of higher
accuracy than the nuclear norm, in this paper, we propose a rank approximation
based on Logarithm-Determinant. We consider using this rank approximation for
subspace clustering application. Our framework can model different kinds of
errors and noise. Effective optimization strategy is developed with theoretical
guarantee to converge to a stationary point. The proposed method gives
promising results on face clustering and motion segmentation tasks compared to
the state-of-the-art subspace clustering algorithms.