Learning low-rank output kernels

Output kernel learning techniques allow to simultaneously learn a vector-valued function and a positive semidefinite matrix which describes the relationships between the outputs. In this paper, we introduce a new formulation that imposes a low-rank constraint on the output kernel and operates directly on a factor of the kernel matrix. First, we investigate the connection between output kernel learning and a regularization problem for an architecture with two layers. Then, we show that a variety of methods such as nuclear norm regularized regression, reduced-rank regression, principal component analysis, and low rank matrix approximation can be seen as special cases of the output kernel learning framework. Finally, we introduce a block coordinate descent strategy for learning low-rank output kernels.