A family of kernel anomaly change detectors
This paper introduces the nonlinear extension of the anomaly change detection algorithms in [1] based on the theory of reproducing kernels. The presented methods generalize their linear counterparts, under both the Gaussian and elliptically-contoured assumptions, and produce both improved detection accuracies and reduced false alarm rates. We study the Gaussianity of the data in Hilbert spaces with kernel dependence estimates, provide low-rank kernel versions to cope with the high computational cost of the methods, and give prescriptions about the selection of the kernel functions and their parameters. We illustrate the performance of the introduced kernel methods in both pervasive and anomalous change detection problems involving both real and simulated changes in multi- and hyperspectral imagery. Excellent performance is achieved in terms of detection accuracy, especially when few training examples are available. Results also reveal that the elliptically-contoured assumption may be still valid in Hilbert spaces, particularly when high pervasive distortions mask anomalous targets.