Multi-label Multiple Kernel Learning

We present a multi-label multiple kernel learning (MKL) formulation in which the data are embedded into a low-dimensional space directed by the instance-label correlations encoded into a hypergraph. We formulate the problem in the kernel-induced feature space and propose to learn the kernel matrix as a linear combination of a given collection of kernel matrices in the MKL framework. The proposed learning formulation leads to a non-smooth min-max problem, which can be cast into a semi-infinite linear program (SILP). We further propose an approximate formulation with a guaranteed error bound which involves an unconstrained convex optimization problem. In addition, we show that the objective function of the approximate formulation is differentiable with Lipschitz continuous gradient, and hence existing methods can be employed to compute the optimal solution efficiently. We apply the proposed formulation to the automated annotation of Drosophila gene expression pattern images, and promising results have been reported in comparison with representative algorithms.