Outlier Detection Methods for One-Dimensional Features Based on the Isolation Forest and 2-Means Algorithms

Abstract

In our study, we propose seven methods of detecting outliers in the set of one-dimensional observations. Instead of considering only one-dimensional input data, we use their two-dimensional vector representations, where each representation consists of an original observation and a score obtained through the application of the Isolation Forest (IF) and Extended Isolation Forest (EIF) algorithms. For the corresponding pairs of values, we first implement the $2$ -means clustering method in order to separate them into two clusters and subsequently, we employ different machine learning concepts, such as: the One-Class SVM, the methods based on the idea of conformal scores and conformal prediction sets, or the testing procedures using conformal $p$ -values. For comparison, we also examine the classic clustering algorithms based on the EM algorithm. Our one-dimensional empirical data are generated from mixtures of two distributions. In our numerical experiments, we consider various examples of distribution mixtures. These mixtures display different difficulty levels regarding the issue of outlier identification, range from the mixtures of two Gaussian distributions, through the mixtures of two heavy-tailed distributions. The proposed methods are also applied to four real-world data. All of our computations have been carried out using the R environment.