A local Fisher discriminant analysis can work well for a multimodal problem. However, it often suffers from the undersampled problem, which makes the local within-class scatter matrix singular. We develop a supervised discriminant analysis technique called uncorrelated regularized local Fisher discriminant analysis for image feature extraction. In this technique, the local within-class scatter matrix is approximated by a full-rank matrix that not only solves the undersampled problem but also eliminates the poor impact of small and zero eigenvalues. Statistically uncorrelated features are obtained to remove redundancy. A trace ratio criterion and the corresponding iterative algorithm are employed to globally solve the objective function. Experimental results on four famous face databases indicate that our proposed method is effective and outperforms the conventional dimensionality reduction methods.
"Uncorrelated regularized local Fisher discriminant analysis for face recognition," Journal of Electronic Imaging 23(4), 043017 (4 August 2014). https://doi.org/10.1117/1.JEI.23.4.043017