A randomized heuristic for kernel parameter selection with large-scale multi-class data

Over the past few years kernel methods have gained a tremendous amount of attention as existing linear algorithms can easily be extended to account for highly non-linear data in a computationally efficient manner. Unfortunately most kernels require careful tuning of intrinsic parameters to correctly model the distribution of the underlying data. For large-scale problems the multiplicative scaling in time complexity imposed by introducing free parameters in a cross-validation setup will prove computationally infeasible, often leaving pure ad-hoc estimates as the only option. In this contribution we investigate a novel randomized approach for kernel parameter selection in large-scale multi-class data. We fit a minimum enclosing ball to the class means in Reproducing Kernel Hilbert Spaces (RKHS), and use the radius as a quality measure of the space, defined by the kernel parameter. We apply the developed algorithm to a computer vision paradigm where the objective is to recognize 72.000 objects among 1.000 classes. Compared to other distance metrics in the RKHS we find that our randomized approach provides better results together with a highly competitive time complexity.