The correntropy MACE filter

Abstract

The minimum average correlation energy (MACE) filter is well known for object recognition. This paper proposes a nonlinear extension to the MACE filter using the recently introduced correntropy function. Correntropy is a positive definite function that generalizes the concept of correlation by utilizing second and higher order moments of the signal statistics. Because of its positive definite nature, correntropy induces a new reproducing kernel Hilbert space (RKHS). Taking advantage of the linear structure of the RKHS it is possible to formulate the MACE filter equations in the RKHS induced by correntropy and obtained an approximate solution. Due to the nonlinear relation between the feature space and the input space, the correntropy MACE (CMACE) can potentially improve upon the MACE performance while preserving the shift-invariant property (additional computation for all shifts will be required in the CMACE). To alleviate the computation complexity of the solution, this paper also presents the fast CMACE using the fast Gauss transform (FGT). We apply the CMACE filter to the MSTAR public release synthetic aperture radar (SAR) data set as well as PIE database of human faces and show that the proposed method exhibits better distortion tolerance and outperforms the linear MACE in both generalization and rejection abilities.