  Multi-task learning has been observed by many researchers, which supposes
that different tasks can share a low-rank common yet latent subspace. It means
learning multiple tasks jointly is better than learning them independently. In
this paper, we propose two novel multi-task learning formulations based on two
regularization terms, which can learn the optimal shared latent subspace by
minimizing the exactly $k$ minimal singular values. The proposed regularization
terms are the more tight approximations of rank minimization than trace norm.
But it's an NP-hard problem to solve the exact rank minimization problem.
Therefore, we design a novel re-weighted based iterative strategy to solve our
models, which can tactically handle the exact rank minimization problem by
setting a large penalizing parameter. Experimental results on benchmark
datasets demonstrate that our methods can correctly recover the low-rank
structure shared across tasks, and outperform related multi-task learning
methods.
