Normalized residual-based constant false-alarm rate outlier detection

•Definition of the normalized residual for the supervised case.•A sufficiently training strategy is introduced to determine the outlier threshold.•A constant false-alarm rate outlier detection method is proposed.•Perfect theory is built for the proposed method.

Outlier detection is an important issue in machine learning and knowledge discovery. The aim is to find the patterns that deviate too much from others. In this paper, we consider constant false-alarm rate (CFAR) outlier detection, and propose a supervised detection method based on normalized residual (NR). For a query point, its NR value related to the training data is compared with a predefined threshold, indicating if it is an outlier. Heretofore, the choice of outlier threshold relied too much on experience, making CFAR detection impossible. We solve the problem by introducing a sufficiently training strategy applying to the given normal instances, gaining a large number of NR values of them, based on which the threshold can be located properly according to the desired false-alarm rate. Theoretical analysis proves that the proposed method can achieve CFAR detection and the most powerful test, regardless of pattern dimension and noise distribution, thus can be widely applied to outlier detection problems. Simulations and real-world data experiments also show that, the proposed method can effectively control the false-alarm rate even when a few training instances are available, and at the same time its operating characteristic is generally better than competing methods.

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