Discriminative kernel hat matrix: A new tool for automatic outlier identification

Identifying outlying observations in data sets is one of the classical topics in robust statistics. We propose to solve this problem by a new one-class kernel Fisher criterion based on the statistics of the subspace decomposition of the kernel hat matrix diagonal. This work extends the recent study proposed in [1] to the nonlinear case. We show here that the maximization of this new contrast measure comes down to search an optimal projection subspace and an optimal indicator matrix. Next, we derive a separating boundary between the dominant population and outliers. We show that the maximum of the criterion corresponds both to an optimal value of the kernel parameters and to an optimal classification providing the expected fraction of outliers. This means that these two problems are intimately related. Synthetic and real data sets are used to study the performance of the proposed approach.