Detection of Outliers in Univariate Circular Data by Means of the Outlier Local Factor (LOF)

The problem of outlier detection in univariate circular data was the object of increased interest over the last decade. New numerical and graphical methods were developed for samples from different circular probability distributions. The main drawback of the existing methods is, however, that they are distribution-based and ignore the problem of multiple outliers. The local outlier factor (LOF) is a density-based method for detecting outliers in multivariate data and it depends on the local density of every k nearest neighbours. The aim of this paper is to extend the application of the LOF to the detection of possible outliers in circular samples, where the angles of circular data are represented in two Cartesian coordinates and treated as bivariate data. The performance of the LOF is compared against other existing numerical methods by means of a simulation based on the power of a test and the proportion of correct detection. The LOF performance is compatible with the best existing discordancy tests, while outperforming other tests. The level of the LOF performance is directly related to the contamination and concentration parameters, while having an inverse relationship with the sample size. In order to illustrate the process, the LOF and other existing discordancy tests are applied to detect possible outliers in two common real circular datasets.