Fuzzy Granule Density-Based Outlier Detection With Multi-Scale Granular Balls

Outlier detection refers to the identification of anomalous samples that\ndeviate significantly from the distribution of normal data and has been\nextensively studied and used in a variety of practical tasks. However, most\nunsupervised outlier detection methods are carefully designed to detect\nspecified outliers, while real-world data may be entangled with different types\nof outliers. In this study, we propose a fuzzy rough sets-based multi-scale\noutlier detection method to identify various types of outliers. Specifically, a\nnovel fuzzy rough sets-based method that integrates relative fuzzy granule\ndensity is first introduced to improve the capability of detecting local\noutliers. Then, a multi-scale view generation method based on granular-ball\ncomputing is proposed to collaboratively identify group outliers at different\nlevels of granularity. Moreover, reliable outliers and inliers determined by\nthe three-way decision are used to train a weighted support vector machine to\nfurther improve the performance of outlier detection. The proposed method\ninnovatively transforms unsupervised outlier detection into a semi-supervised\nclassification problem and for the first time explores the fuzzy rough\nsets-based outlier detection from the perspective of multi-scale granular\nballs, allowing for high adaptability to different types of outliers. Extensive\nexperiments carried out on both artificial and UCI datasets demonstrate that\nthe proposed outlier detection method significantly outperforms the\nstate-of-the-art methods, improving the results by at least 8.48% in terms of\nthe Area Under the ROC Curve (AUROC) index. { The source codes are released at\n\\url{https://github.com/Xiaofeng-Tan/MGBOD}. }\n