A Convergent Solution to Matrix Bidirectional Projection Based Feature Extraction with Application to Face Recognition

Recently, many feature extraction methods, which are based on the matrix representation of image and matrix bidirectional projection technique, are proposed. However, these methods in solving the two projection matrices will suffer from non-optimized or non-convergent solution. To overcome this problem, a novel feature extraction method which exploits the Maximum Margin Criterion is proposed, where an iterative optimization algorithm is designed to compute the two projection matrices. A noteworthy property of the proposed iterative solution algorithm is that it can monotonously increase the optimization objective, i.e., the bidirectional projection margin. According to this property, we further theoretically prove that the objective value and the solution are convergent. Moreover, the proposed method can automatically determine suitable feature dimensionality to obtain competitive recognition performance. Extensive and systematic experiments on CMU PIE and Yale face databases demonstrate the high convergence speed of the proposed iterative optimization procedure, as well as the superiority of the proposed feature extraction method over other state-of-the-art approaches in face recognition. © 2011, the authors.