Kernel Conjugate Gradient

We propose a novel variant of conjugate gradient based on the Reproducing Kernel Hilbert Space (RKHS) inner product. An analysis of the algorithm suggests it enjoys better performance properties than standard iterative methods when applied to learning kernel machines. Experimental results for both classification and regression bear out the theoretical implications. We further address the dominant cost of the algorithm by reducing the complexity of RKHS function evaluations and inner products through the use of space-partitioning tree data-structures.