Improved subspace-based and angle-based outlier detections for fuzzy datasets with a real case study

Abstract

To overcome curse of dimensionality for outlier detecting in high dimensional dataset, axis-parallel subspace (SOD) and angle-based outlier detection (ABOD) methods were presented. These methods are also friendly used distance-based to detect outliers. In this regard, based on the reality of fuzzy data for explaining the world phenomena, this paper introduces an extended version of both methods for fuzzy dataset. First, the basic concepts of both methods are explained. Next we provide two metrics based on Euclidean and analytic distance to measure distance between fuzzy objects; also Cosine similarity measure formula for calculating the cosine of angle between two difference vectors in high-dimensional fuzzy dataset is illustrated. Then the algorithms to determine outliers of fuzzy datasets by using these metrics and Cosine similarity measure, based on ABOD and SOD algorithms, are presented. Some numerical experimental examples are also presented, in which both real and synthesis datasets are used, For a real numerical examination, we have applied proposed algorithms to data from 15 Iranian petrochemical companies in a fully fuzzy environment. The obtained results show the significant properties of the new methods in detecting outliers.