How to Estimate the Regularization Parameter for Spectral Regression Discriminant Analysis and its Kernel Version?

Spectral regression discriminant analysis (SRDA) has recently been proposed as an efficient solution to large-scale subspace learning problems. There is a tunable regularization parameter in SRDA, which is critical to algorithm performance. However, how to automatically set this parameter has not been well solved until now. So this regularization parameter was only set to be a constant in SRDA, which is obviously suboptimal. This paper proposes to automatically estimate the optimal regularization parameter of SRDA based on the perturbation linear discriminant analysis (PLDA). In addition, two parameter estimation methods for the kernel version of SRDA are also developed. One is derived from the method of optimal regularization parameter estimation for SRDA. The other is to utilize the kernel version of PLDA. Experiments on a number of publicly available databases demonstrate the effectiveness of the proposed methods for face recognition, spoken letter recognition, handwritten digit recognition, and text categorization.