| The major goal of my research was to develop nonlinear methods of the family of distortion invariant filters, specifically the minimum average correlation energy (MACE) filter. The minimum average correlation energy (MACE) filter is a well known correlation filter for pattern recognition. My research investigated a closed form solution of the nonlinear version of the MACE filter using the recently introduced correntropy function.Correntropy is a positive definite function that generalizes the concept of correlation by utilizing 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 and solve the MACE filter equations in the RKHS induced by correntropy. 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, my research also presents the fast CMACE using the Fast Gauss Transform (FGT). Both the MACE and CMACE are basically memory-based algorithms and due to the high dimensionality of the image data, the computational cost of the CMACE filter is one of critical issues in practical applications. Therefore, my research also used a dimensionality reduction method based on random projections (RP), which has emerged as a powerful method for dimensionality reduction in machine learning.We applied the CMACE filter to face recognition using facial expression data and the MSTAR public release Synthetic Aperture Radar (SAR) data set, and experimental results show that the proposed CMACE filter indeed outperforms the traditional linear MACE and the kernelized MACE in both generalization and rejection abilities. In addition, simulation results in face recognition show that the CMACE filter with random projection (CMACE-RP) also outperforms the traditional linear MACE with small degradation in performance, but great savings in storage and computational complexity. |
