Maximum Margin/Volume Outlier Detection

Due to the absence or scarcity of outliers, designing a robust outlier detector is very challenging. In this paper, we first propose to use the maximum margin criterion to sift unknown outliers from a given data set, which demonstrates superior performance in outlier detection. However, the resultant learning task is formulated as a Mixed Integer Programming (MIP) problem, which is computationally hard. To this end, we alter the recently developed label generating technique, which efficiently solves a convex relaxation of the MIP problem of outlier detection. Specifically, we propose an effective procedure to find a largely violated labeling vector for identifying rare outliers from abundant normal patterns, and its convergence is also presented. Then, a set of largely violated labeling vectors are combined by multiple kernel learning methods to robustly detect outliers. Besides these, to further enhance the efficacy of our outlier detector, we also explore the use of maximum volume criterion to measure the quality of separation between outliers and normal patterns. This criterion can be easily incorporated into our proposed framework by introducing an additional regularization. Comprehensive experiments on real-world data sets verify that the outlier detectors using the two proposed criteria outperform existing outlier detection methods.