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.

In many real world applications data is collected in multi-dimensional spaces, with the knowledge hidden in subspaces (i.e., subsets of the dimensions). It is an open research issue to select meaningful subspaces without any prior knowledge about such hidden patterns. Standard approaches, such as pairwise correlation measures, or statistical approaches based on entropy, do not solve this problem; due to their restrictive pairwise analysis and loss of information in discretization they are bound to miss subspaces with potential clusters and outliers. In this paper, we focus on finding subspaces with strong mutual dependency in the selected dimension set. Chosen subspaces should provide a high discrepancy between clusters and outliers and enhance detection of these patterns.

In many real-world applications, data is collected in multi-dimensional spaces. However, not all dimensions are relevant for data analysis. Instead, interesting knowledge is hidden in correlated subsets of dimensions (i.e., subspaces of the original space). Detecting these correlated subspaces independent of the underlying mining task is an open research problem. It is challenging due to the exponential search space.