Parameter k search strategy in outlier detection

The selection for parameter k(the number of nearest neighbors) is an important problem in the field of outlier detection. If k selected is too small, outlier clusters may not be detected. On the contrary, normal points may be detected as outliers. In order to solve the parameter selection problem, recent studies select k by searching for a natural or stable relative neighborhood. However, these studies intuitively chose k, and haven't explained why the k is appropriate. In this paper, we have analyzed the above questions and presented a mutual neighbor graph(MNG) based parameter k searching algorithm. Furthermore, we proved the chosen k is appropriate from three angles. Experiments on synthetic and real data sets demonstrate that the proposed method achieves better performance than other alternatives.