Kernel-based regularization discriminant analysis (KRDA) is one of the promising approaches for solving small sample size problem in face recognition. This paper addresses the problem in regularization parameter reduction in KRDA. From computational complexity point of view, our goal is to develop a KRDA algorithm with minimum number of parameters, in which regularization process can be fully controlled. Along this line, we have developed a Kernel 1-parameter RDA (K1PRDA) algorithm (W. S. Chen, P C Yuen, J Huang and D. Q. Dai, "Kernel machine-based one-parameter regularized Fisher discriminant method for face recognition," IEEE Transactions on SMC-B, to appear, 2005.). K1PRDA was developed based on a three-parameter regularization formula. In this paper, we propose another approach to formulate the one-parameter KRDA (1PRKFD) based on a two-parameter formula. Yale B database, with pose and illumination variations, is used to compare the performance of 1PRKFD algorithm, K1PRDA algorithm and other LDA-based algorithms. Experimental results show that both 1PRKFD and K1PRDA algorithms outperform the other LDA-based face recognition algorithms. The performance between 1PRKFD and K1PRDA algorithms are comparable. This concludes that our methodology in deriving the one-parameter KRDA is stable.
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