A Unified Convex Surrogate for the Schatten-$p$ Norm

  title={A Unified Convex Surrogate for the Schatten-\$p\$ Norm},
  author={Chen Xu and Zhouchen Lin and Hongbin Zha},
The Schatten-p norm (0 < p < 1) has been widely used to replace the nuclear norm for better approximating the rank function. However, existing methods are either 1) not scalable for large scale problems due to relying on singular value decomposition (SVD) in every iteration, or 2) specific to some p values, e.g., 1/2, and 2/3. In this paper, we show that for any p, p1, and p2 > 0 satisfying 1/p = 1/p1 + 1/p2, there is an equivalence between the Schatten-p norm of one matrix and the Schatten-p1… CONTINUE READING
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