Class-consistent technology-based outlier detection for incomplete real-valued data based on rough set theory and granular computing

Abstract The goal of outlier detection is to pinpoint data points that exhibit notable deviations from the rest of the observed values. It has found successful application in numerous fields, including process inspection, anti-terrorist operations, and public security. However, the majority of existing outlier algorithms rely on methods involving filling or deleting missing data, with few directly addressing incomplete data. This article studies outlier detection for incomplete real-valued data based on class-consistent technology, rough set theory, and granular computing. First, a tolerance relation founded on class-consistent technology is presented to illustrate the similarity among information values within an incomplete real-valued information system (IRVIS). Then, the tolerance classes are established based on the tolerance relation and utilized for computing approximate accuracy and other metrics. Next, an outlier factor is defined, considering both the degree of outlierness and the weight function assigned to each object within an IRVIS, elucidating the uncertainty and degree of outlier. Finally, an outlier detection algorithm (ODIRG) for an IRVIS based on class-consistent technology, rough set theory, and granular computing is devised. Numerical experiments on seven UCI datasets are undertaken to evaluate the stability of the ODIRG algorithm. The proposed method is demonstrated to exhibit strong effectiveness and adaptability for categorical data when compared with five other algorithms. It is notable that for comprehensive comparison, precision, recall, <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>F</m:mi> </m:math> F 1-measure, and receiver operating characteristic curve are employed to delineate the benefits of the proposed approach.