An optimal set of code words and correntropy for rotated least squares regression

This paper presents a robust feature extraction method for face recognition based on least squares regression (LSR). Our focus is to enhance the robustness and discriminability of the LSR. First, an optimal set of code words is introduced in LSR. Compared to the traditional set of code words, this new set uses less number of code words. Furthermore, it can make the distance of the regression targets of different classes as large as possible. Then, correntropy is integrated into the LSR model for better robustness. Furthermore, considering the commonly used distance metrics such as Euclidean distance and Cosine distance in the subspace are invariant to rotation transformation, rotation is introduced as additional freedom to promote flexibility without sacrificing accuracy. Our objective function is optimized using half-quadratic (HQ) optimization, which facilitates algorithm development and convergence study. Experimental results show that our method outperforms several subspace methods for face recognition, which indicates the validity of the proposed method.