A Quality Index for Detection of Atypical Elements (Outliers)

Besides clustering and classification, detection of atypical elements (outliers, rare elements) is one of the most fundamental problems in contemporary data analysis. However, contrary to clustering and classification, an atypical element detection task does not possess any natural quality (performance) index. The subject of the research presented here is the creation of one. It will enable not only evaluation of the results of a procedure for atypical element detection, but also optimization of its parameters or other quantities. The investigated quality index works particularly well with frequency types of such procedures, especially in the presence of substantial noise. Using a nonparametric approach in the design of this index practically frees the proposed method from the distribution in the dataset under examination. It may also be successfully applied to multimodal and multidimensional cases.