Isolation Set-Kernel and Its Application to Multi-Instance Learning

Set-level problems are as important as instance-level problems. The core in solving set-level problems is: how to measure the similarity between two sets. This paper investigates data-dependent kernels that are derived directly from data. We introduce Isolation Set-Kernel which is solely dependent on data distribution, requiring neither class information nor explicit learning. In contrast, most current set-similarities are not dependent on the underlying data distribution. We theoretically analyze the characteristic of Isolation Set-Kernel. As the set-kernel has a finite feature map, we show that it can be used to speed up the set-kernel computation significantly. We apply Isolation Set-Kernel to Multi-Instance Learning (MIL) using SVM classifier, and demonstrate that it outperforms other set-kernels or other solutions to the MIL problem.