Learning Output Kernels with Block Coordinate Descent

We propose a method to learn simultaneously a vector-valued function and a \nkernel between its components. The obtained kernel can be used both to improve \nlearning performance and to reveal structures in the output space which may be \nimportant in their own right. Our method is based on the solution of a suitable \nregularization problem over a reproducing kernel Hilbert space of vector-valued \nfunctions. Although the regularized risk functional is non-convex, we show that \nit is invex, implying that all local minimizers are global minimizers. We \nderive a block-wise coordinate descent method that efficiently exploits the \nstructure of the objective functional. Then, we empirically demonstrate that \nthe proposed method can improve classification accuracy. Finally, we provide a \nvisual interpretation of the learned kernel matrix for some well known \ndatasets.