An Outlier Fuzzy Detection Method Using Fuzzy Set Theory

Outlier mining task is to discover some unusual objects, and however, most existing methods and their mining results lack pertinence. To address the pertinence of outlier results, we propose a novel outlier detection approach, namely, FOD, which aims at finding anomalies in full dimensions that lack pertinence and understandability. Our key idea is to use fuzzy constraint technology to prune irrelevant objects for outlier detection, during which the nearness measure theory in fuzzy mathematics is used for detecting similarities between objects and constraint information. FOD finds outlier by searching sparse subspace, where genetic algorithms can be extended and incorporated into FOD such that an optimum solution of an anomaly is discovered. While constructing a sparse subspace, we present the sparse threshold concept to describe the sparse levels of data objects in a subspace, where data objects are regarded as anomalies. Then, we demonstrate the effectiveness and scalability of our method on synthetic and UCI datasets. The experiment evaluations reveal that our fuzzy constraint-based outlier detection is superior to two existing full dimensional algorithms. Moreover, FOD algorithm also improves the accuracy of outlier detection.