Spectral k-Support Norm Regularization

The $k$-support norm has successfully been applied to sparse vector prediction problems. We observe that it belongs to a wider class of norms, which we call the box-norms. Within this framework we derive an efficient algorithm to compute the proximity operator of the squared norm, improving upon the original method for the $k$-support norm. We extend the norms from the vector to the matrix setting and we introduce the spectral $k$-support norm. We study its properties and show that it is closely related to the multitask learning cluster norm.