New Perspectives on $k$-Support and Cluster Norms

摘要: We study a regularizer which is defined as parameterized infimum of quadratics, and we call the box-norm. show that k-support norm, proposed by [Argyriou et al, 2012] for sparse vector prediction problems, belongs to this family, box-norm can be generated perturbation former. derive an improved algorithm compute proximity operator squared box-norm, provide method norm. extend norms matrices, introducing spectral norm note essentially equivalent cluster multitask learning introduced [Jacob al. 2009a], in turn interpreted Centering important also use centered versions regularizers. Numerical experiments indicate box-norms their variants state art performance matrix completion problems respectively.