Improving classification performance of linear feature extraction algorithms

In this work, we propose a new and novel framework for improving the performance of linear feature extraction (LFE) algorithms, characterized by the Bayesian error probability (BEP) in the extracted feature domain. The proposed framework relies on optimizing a tight quadratic approximation to the BEP in the transformed space with respect to the transformation matrix. Applied to many synthetic multi-class Gaussian classification problems, the proposed optimization procedure significantly improves the classification performance when it is initialized by popular LFE matrices such as the Fisher linear discriminant analysis.