Fusing fuzzy rough sets and mean shift for anomaly detection

Abstract

Outlier detection is a critical but challenging task due to the complex distribution of practical data, and some Fuzzy Rough Sets (FRS)-based methods have been presented to identify outliers from these data. However, these methods still have limitations when facing the co-existence of different types of outliers. In this study, an improved FRS-based unsupervised anomaly detection method is proposed by integrating distance and density information. Specifically, to detect the local outliers, a fuzzy granule density is first defined by introducing a Gaussian kernel similarity to characterize the local density of samples. Then, optimistic and pessimistic fuzzy granule densities are further developed to evaluate the density variation in the local neighborhood. Moreover, a distance measure based on mean shift is introduced to detect global and group outliers. Finally, an outlier detection method that integrates the density and distance measures is designed to effectively identify diverse types of outliers. Extensive experiments on synthetic and public datasets, along with statistical significance analysis, demonstrate the superior performance of the proposed method, achieving an average improvement of at least 12.27% in terms of AUROC.