Isolation Kernel and Its Effect on SVM

Kai Ming Ting, Yue Zhu, Zhi-Hua Zhou

Abstract: This paper investigates data dependent kernels that are derived directly from data. This has been an outstanding issue for about two decades which hampered the development of kernel-based methods. We introduce Isolation Kernel which is solely dependent on data distribution, requiring neither class information nor explicit learning to be a classifier. In contrast, existing data dependent kernels rely heavily on class information and explicit learning to produce a classifier. We show that Isolation Kernel approximates well to a data independent kernel function called Laplacian kernel under uniform density distribution. With this revelation, Isolation Kernel can be viewed as a data dependent kernel that adapts a data independent kernel to the structure of a dataset. We also provide a reason why the proposed new data dependent kernel enables SVM (which employs a kernel through other means) to improve its predictive accuracy. The key differences between Random Forest kernel and Isolation Kernel are discussed to examine the reasons why the latter is a more successful tree-based kernel.