Fusion of correntropy and mean square error for sparse representaion based classification

By representing the input test sample as a sparse linear combination of the training samples via ℓ₁-norm minimization, sparse representation based classification (SRC) has been successfully applied to pattern classification recently. In SRC, the representation fidelity to the test sample is measured by mean square error (MSE) criterion and it can find the optimal solution when the reconstruction residual follows Gaussian distribution. More recently, correntropy-based sparse representation (CESR), which can effectively deal with non-Gaussian noise and impulsive noise, is proposed for robust pattern classification. The SRC algorithm can achieve better classification performance when the test samples are clean, i.e. without noise or outliers, whereas the CESR algorithm can achieve better performance when the test samples are corrupted by noise, e.g. occlusion, corruption. By utilizing the advantages of these two algorithms, we propose a new model called fusion of correntropy and MSE for sparse representation based classification (FCMSR) in this paper. By combining the global MSE criterion and the local correntropy criterion, the sparse representation coefficients calculated by FCMSR can describe the relationship between the test sample and the training samples more accurately, leading to a better classification performance. Experiments on JAFFE and Cohn-Kanade databases testify the effectiveness of our algorithm.