Extended Isolation Forest

We present an extension to the model-free anomaly detection algorithm, Isolation Forest. This extension, named Extended Isolation Forest (EIF), resolves issues with assignment of anomaly score to given data points. We motivate the problem using heat maps for anomaly scores. These maps suffer from artifacts generated by the criteria for branching operation of the binary tree. We explain this problem in detail and demonstrate the mechanism by which it occurs visually. We then propose two different approaches for improving the situation. First we propose transforming the data randomly before creation of each tree, which results in averaging out the bias. Second, which is the preferred way, is to allow the slicing of the data to use hyperplanes with random slopes. This approach results in remedying the artifact seen in the anomaly score heat maps. We show that the robustness of the algorithm is much improved using this method by looking at the variance of scores of data points distributed along constant level sets. We report AUROC and AUPRC for our synthetic datasets, along with real-world benchmark datasets. We find no appreciable difference in the rate of convergence nor in computation time between the standard Isolation Forest and EIF.