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We present Random Partition Kernels, a new class of kernels derived bydemonstrating a natural connection between random partitions of objects andkernels between those objects. We show how the construction can be used tocreate kernels from methods that would not normally be viewed as randompartitions, such as Random Forest. To demonstrate the potential of this method,we propose two new kernels, the Random Forest Kernel and the Fast ClusterKernel, and show that these kernels consistently outperform standard kernels onproblems involving real-world datasets. Finally, we show how the form of thesekernels lend themselves to a natural approximation that is appropriate forcertain big data problems, allowing $O(N)$ inference in methods such asGaussian Processes, Support Vector Machines and Kernel PCA.

The Random Forest Kernel and other kernels for big data from random partitions